Heathrow to Conwy - London connections

the gateline should give back your ticket after you put it in, but I wouldn't do that. I would always use a staffed gate and show the ticket to the staff person who will open the gate and do that until the end of your trip.

Remember that Conwy os a Request stop so you will need to arrange with the Train Manager to get off.

What tube route are you taking from Paddington to Euston?

You should be able to pick up your Euston to Conwy ticket at Heathrow ticket machines.

There is no direct route to Euston itself. The tube (Circle line or Hammersmith and City) will take you to Euston Square.

From there it is a 5 minute walk down Euston Road to Euston.

If it is raining stay on to Kings Cross then switch to either the Victoria Line southbound or the Northern line northbound (1 stop on either) to Euston. But the walking makes Euston that way or Euston Square equally easy.
Turn left out of Euston Square tube station (if you come up the stairs on the north side of the road) (right if you come up the elevator on the south side of the road) then walk one city block, cross the street at the traffic lights and head up on to the Piazza to access Euston station. If on the south side of the road you will first have to cross Euston Road at this junction.

If you are using the Elizabeth Line from Paddington switch trains at Tottenham Court Road onto the Northern line to Euston.

The signage is very clear at Paddington to either the tube or the Elizabeth Line. For your through ticketing purposes the Elizabeth Line counts as the tube, although technically it isn't.

You would have been better advised to take the Elizabeth Line all the way from Heathrow to Tottenham Court Road, then switch to Northern Line as above, but you have what you have,

Ok, now I'm confused - my ticket is actually Paddington to Llandudno Junction (I said Conwy, but it's not) and just indicates that the 1st part is the underground to Euston. It seems that there must be many things left out (glad I asked).

Can you recommend a single way as the great and varied info is a bit overwhelming. What would be the least complicated to do?
Thanks

The long distance train from Euston to north wales stops at Llandudno Junction, 1 mile across the bridge from Conwy. Only local trains stop at Conwy.
Get off at Llandudno Junction and jump in a cab- there is a rank at the station.

Don't bother waiting for a local train over the bridge to Conwy. The taxi is faster, and will take you straight to the hotel.

As you don't know where you are going I would take the Elizabeth Line from Paddington to Tottenham Court Road, switch to the Northern line northbound 3 stops to Euston.

When you come off the Heathrow Express at Paddington (Platform 6 or 7), at the end of the platform turn right to the end, then right down Platform 1, The EL entrance is on your left just before the First Class lounge. Plan here - https://www.networkrail.co.uk/wp-content/uploads/2023/08/London-Paddington-Station-Map.pdf

Memo to other future readers- buy a through ticket Heathrow to Conwy and take the Elizabeth Line at Heathrow.

Be aware.. .there is no step free access from the Northern line up to Euston station. .I found that out the hard way.

which Northern Line, Frank II?

Northbound on the Charing Cross Branch at the middle of the first car, turn right, then follow the passageways to the escalator banks, up one quite long one, then from the ticket hall up another medium sized, into the concourse. Am I misremembering?

True, if using the shortcut to The Wood (our name for platforms 8-11 inclusive) there are stairs, but if you go up and over you can get to any platform.

I am the first to admit not regularly having used Charing Cross Branch southbound, nor either direction on the Northern Line Bank Branch from Euston.

The OP has not even asked for step free access.

Transport for London confirm that Northern Line platforms to main line station is all escalators. Tottenham Court Road is on the Charing Cross branch of the Northern Line. But the Bank branch also has escalators all the way up.

The attempt here is to give the simplest route on the tube, rather than having the OP getting lost on Euston Road.

I will definitely want elevator or escalator - 74 with a suitcase...

Thanks for all the input. I'm pretty experienced in public transit having used it in a number of European cities (and living in Chicago), so I'm sure I'll be fine. It did seem, from the ticket, that I could just go from Paddington to Euston Station, so good to know there's a bit more to it.