Heathrow to Manchester

I'm sure someone else can advise on the bus, which I have never taken... but let me advise o timing.

Heathrow arrivals are a little difficult to time - some factors include the distance from your gate to passport control, and how long they take to get luggage offloaded, but in general I would allow an hour from landing to getting to the tube station (which is a little bit of a walk in itself and there are sometimes delays waiting for lifts due to the number of passengers).

It's about and hour by tube to central London, and even with the change to get to Euston, you have plenty of time.

Yes, rhe tube very easy to travel on- tap your contactless card at the barriers (each passenger needs their own payment form).

When you get to Euston, check the big boards for your train. The platform will be indicated 15 minutes or so before departure. Make sure you board the train immediately so you get enough space to store your luggage.

Staff at the tube stations and train stations are normally very helpful, so if you get lost just ask.

Basically you have things right. Leaving 4 hours between landing at LHR and the train from Euston should be perfectly fine. It's likely that the transfer will take quite a bit less than 4 hours but there is a risk that booking an earlier train with an Advance ticket runs the risk of you missing it and having to buy new tickets at the walk-up price. £50 tickets will be Advance singles - you must travel on the train you book. There are plenty of places to sit, eat and drink at Euston.
It's not the Subway, that's a pedestrian underpass or a sandwich shop in the UK. What you want is officially the Underground but is universally known as the Tube. Don't worry about platform numbers - you won't see any. Just head for the Underground at LHR and take any train - there is only one line there and all trains will go to Green Park, even if they are not going all the way to Cockfosters. The same with the change at Green Park, just look for the Victoria Line. A tip at Green Park - don't follow the signs to the Victoria line on the platform but follow the exit. This will take you up an escalator where you then look for another down to the Victoria line. It's quicker than a long underground walk.
How old is the other person in the group? If a child under 16 then you may well benefit from buying a Friends & Family railcard. Whether you will depends on what other rail travel you are planning. The card costs £35 and will give adults 1/3rd off any train ticket and children 60% off. So taking your train to Manchester - I see tickets at £49.50 for your date right now - you will save more than the cost of the pass. Then any other train travel will be discounted too.
If you have a child under 5 then it will be better to buy a Two Together railcard. This is for any two specific people travelling together - costs the same at £35 and the same 1/3rd discount and an under 5 travels for free.
You can buy either railcard online or in person at a station. You can book rail tickets now saying that you have a railcard, you only need to actually have it when boarding your first train.

The subway in London is called the London Underground or tube. If you ask for directions to the subway you will end up at a Subway. Yes, like Starbucks there are Subways, McDonalds, and Burger King franchises there.

Will make your trip easier if you use the proper vernacular.

Have traveled to London from the West Coast for decades. Arrival and clearing immigration is always a crap shoot. Truly depends on the staffing. The longest it’s taken was an hour, the shortest 15 minutes.

Using the tube is easy once you get the hang of it. The tube is also a space where quiet is expected and appreciated, chatting on your phone, talking, listening to music, watching a movie on your phone without headphones are signs of borish behavior.

Remember when on the escalators or climbing stairs please stand or walk on the right. Also outside on the busy streets you ‘ll need a moment for your brain to adapt to the traffic flow which is the opposite of you are used to. Thus be smart, don’t follow the crowds, wait for the lights to change before crossing.

Great city. Appreciate and respect the differences.

National Express would be an alternative and pretty frequent - the only problem is that you always have to change bus at either Birmingham or Milton Keynes Coachway. Because it is from an airport it isn't that cheap either- direct buses from London Victoria are way cheaper.
Clearly it takes a lot longer than the train, especially because of the change. Both MK and Birmingham are nice coach stations with refreshments and pay to use toilets..
If you book the bus ahead (rather than on the day when you arrive) then add the change option for another £5 each.
With a train every 20 minutes to Manchester, you could just buy a ticket when you arrive. The most you can pay before 4pm is £42.90 each if you take the hourly London North Western semi fast train to Crewe at 46 past the hour, changing at Crewe onto the hourly Transport for Wales train or the twice hourly Northern train to Manchester.
Even in the peak an Anytime Single by that route is only £70.
That is cheaper and faster than National Express.

Just a few random thoughts.
Having lived in London for a long time I would always allow more time than journey planners quote for a journey. If nothing else they never seem to factor in enough time to get to, and transfer between, platforms.

The tube can on occasion have problems and delays so it is worth having a plan in your back pocket on how you will get there if the Piccadilly line isn’t working. For example, Heathrow Express or Elizabeth line into town. The Citymapper app can really help with making public transport travel decisions on the fly so it’s worth having it on your phone before you arrive.

To put it politely Euston is not the best station for ‘traveller experience’. It can be bloody awful although if you are there in the middle of the day as you plan it shouldn’t be too busy. One thing to be aware of is there is often very little time between the announcement of a train’s platform and the departure time. You need to be prepared to move as soon as the platform is announced and also be prepared to manoeuvre within and between crowds of people. Make sure everyone knows what carriage you are aiming for in case you get split up. I don’t want it to sound too bad but if you are not use to busy train stations it’s worth being aware.

If you do decide to travel on a NorthWestern train rather than Avanti they don’t have catering. If you want to get a drink or snacks for the journey you will need to get them before you get on the train. There are lots of options at Euston.

A few thoughts from me:

-It is really hard to predict how long it will be from landing to exiting Heathrow, and that's assuming your flight lands on time. I would build in a lot of extra time if you want to book a train departing the same day.
-My preference is not to use the tube to get in from the airport. It takes forever and there is nowhere to put your luggage. I would either take Heathrow Express to Paddington and then Hammersmith and City or Circle line to Euston or I would take the Elizabeth Line to Tottenham Court Road and then the Northern line to Euston. If you buy Heathrow Express ahead of time it's not so expensive. For Elizabeth Line you can just tap and go.
-Emma is absolutely right about Euston station, it's not one of our nicer ones. Just be aware they may not announce/post the platform number until right before the train is due to depart.

IME you get adequate notice of your platform, at least 15 minutes and it only takes 3-4 minutes from the main hall to your train. The smokers/vapers will be outside watching their boards but I would advise that you watch from the main hall, as soon as you see your platform number, just head for the appropriate one. the trains that I have used have always gone from either 3 or 4, others may tell us if this changes much.

You won’t need your ETA documents on arrival (other than passport of course), although it’s good to have them just in case, since your airline from Canada would have checked that and you wouldn’t have been allowed to board your flight without an ETA approval.

I don't see any particular issues with luggage on the Piccadilly Line. You will be getting on where the trains starts so are guaranteed seats and some space near doors to put luggage. The Elizabeth Line is a good alternative - it is more comfortable and quicker but more expensive and wherever you change is a bit awkward. Taking the Hammersmith & City or Circle lines from Paddington means quite a walk at Paddington from the Elizabeth Line and a walk from Euston Square station to Euston itself. Changing at Tottenham Court Road means that exiting at Euston you have 20-30 steps to climb.

I am extremely familiar with taking Avanti trains from Euston. It's true that you do not get a lot of notice of which platform will be used but it is always at least 10 minutes and often a bit more. If you have seats reserved there is no need to rush, you will be fine. Especially leaving around 2pm when the trains will not be full.

You will be getting on where the trains starts so are guaranteed seats and some space near doors to put luggage.

That was not my experience in December - after arriving at T5 on BA from LAX, I made my way downstairs and boarded a jam-packed Piccadilly car. I was able to find a seat, with backpack in my lap and 22" roller between my legs. I could see into the car in front of us and observed people standing for the majority of the distance into central London. Of course, YMMV.

On the return I took the Elizabeth Line, which was luxurious by comparison,

I take the same trains as @briwire. Depending on the hour they are scheduled to leave from all over the station, let alone when they are re platforned.
As a regular on the route I know the theoretical platform for each of the Glasgow 's so am always there well before they are advertised.

If you prefer to stand around waiting for a specific Avanti, more expensive than just taking the first available LNWR, then the 1353 Manchester in theory leaves from 13 and the 1413 from Platform 6.

If you land on time and get through Heathrow in good time you have a very good chance of being on the 1246 to Crewe, Crewe 1454/1527 Manchester arrive 1613. There is a slower 1513 from Crewe, arrives Manchester Pic via the Airport at 1628.