Train from Heathrow to St. David's, Wales

This is a bit of a difficult/lengthy journey.

You need to take a bus from Haverfordwest, the last of which is at 1715.

Trains to Haverfordwest generally only run every 2 hours with a few extras. From London you change at Carmarthen.
Only two trains from London get there in time on a weekday- 0948 and 1148 from Paddington.
At a pinch there are later trains to Haverfordwest then a 16 mile taxi ride.

Also an extra at 0848, change at Swansea, not Carmarthen.

The 1248 from Paddington, change Swansea arrives at Haverfordwest at 1712, too tight for the last bus.

Take the Elizabeth Line, or the Heathrow Express, or the Underground from Heathrow to London Paddington

Take a train from London Paddington to Haverfordwest

https://www.nationalrail.co.uk/

Then a bus from Haverfordwest to St Davids

https://bustimes.org/services/t11-fishguard-haverfordwest-2

This is a very long journey taking around 5 hours 40 minutes - and that is just to the nearest station to St.David’s - at Haverfordwest. Then you have the bus journey on top to reach St.David’s.

I suggest that you land at Heathrow and go by train to Cardiff, check in to a hotel so you can dump your baggage and then have a look around that city - see Cardiff Castle and maybe take a bus the 1 mile down to Cardiff Bay (waterside restaurants etc). Then the following day (unless you want to stay longer in Cardiff to visit St.Fagans Castle & Museum and the medieval castle at Caerphilly), take a train (direct trains are available very other hour) to Haverfordwest and on to St.David’s. Also note that direct trains also go from Cardiff to Tenby on the south Pembrokeshire coast.

Regarding to the journey to / from London; journey planners come up with several options with one being to go by Elizabeth Line train the few minutes from Heathrow to Hayes & Harlington and change for another train to Reading where you get the GWR express going west. The other option is to go from Heathrow into Paddington to catch a GWR express. Every other hour, a GWR express goes all the way to Carmarthen (rear 5 coaches only - train splits in Swansea) where you would change again for Haverfordwest. Some GWR express trains only go as far west as Cardiff and others terminate at Swansea - hence the reason why you see varying instructions for your journey regarding places to change trains.

Advance one way tickets are for specific trains and I would be wary of these if you are not sure when you will show up for train. Often, for maybe near the same price, you can get a return ticket - assuming you will be going back on the same route. On weekdays, if you can travel off peak, an off-peak return might be your best option as that gives you the flexibility to use any off peak train. This could cost you £127.20.

Try playing around with this site and click the i symbol for information on the change points as it should make things clearer:>https://trainsplit.com

let's skip all the answers so far and go back to the original question. Why exactly can't you make sense of the train schedules you've found online - and where did you find them?

Once I'm clear on that I'll tell you a simple way to get from Heathrow onto a westbound GWR train......

Let's not skip all the answers so far, I have given you very good information about the Paddington to Haverfordwest section of the journey.
There are multiple ways from Heathrow to join that train, none of which are easiest or best.
It is one of the most vexatious questions on the forum.
The underground is the cheapest but slowest and requires a change, but that may not matter if you have a long time to wait for the next train from Paddington.
Likewise in those circumstances there is nothing wrong with the route to Reading changing at Hayes and Harlington, but if you are tired/jet lagged may not be the best.
The Heathrow Express and Elizabeth Line are direct and easy routes. If you can get an early bird ticket on the Heathrow Express that is the cheaper and faster of the two.
There is also the Rail Air Link bus to Reading Station and pick up the train there. That is fine, but could leave you with a long wait at Reading.
If that happens Paddington has way more facilities (food and drink) than Reading. And you are joining a train at its origin point if you join at Paddington - always a plus point.
In short each route has its pros and cons, and passionate advocate.

In a sense that is what is confusing you. Too many choices for the first leg.

Detach that journey from Heathrow and just look at Paddington to Haverfordwest.

Detaching like that leaves you free to make decisions on the day. Say the Elizabeth Line to Paddington is having problems choose one of the other routes.
You might choose the bus to Reading but that is no good if buses are delayed/cancelled due to an incident on the M4.

whilst we wait for the answer to what I asked, explain how the wait at Reading could be longer than the wait at Paddington when they are the same trains and frequencies?

Firstly the original question asked for any suggestions or thoughts, not what someone (anyone) perceives to be the best way.

That is exactly what other people have done, in a succinct way.

It has not been said that the wait is any longer at Reading than Paddington.

However this is not like Bath or Oxford where you will only ever have a short wait for the next train. Here we have 2 hour service gaps.

And Reading station does have far fewer facilities than Paddington.

The longer journey time of the Reading bus (and poorer frequency) versus the Elizabeth Line or Heathrow Express to Paddington then the high speed train Paddington to Reading makes journey times pretty much a wash between Paddington and Reading time wise.
If service was normal, and I was tight for time on such a frequency I would rather gamble on the train than the M4 motorway.
If I was tight for time I might even feel that £25 on the Heathrow Express was a better investment than £12.90 on the Elizabeth Line.
In the overall context of the trip £12 is nothing.

I know the OP asked for rail options, but National Express has good bus options direct from Heathrow changing at Newport (Gwent) or Swansea.
I know the bus and rail stops at both are not adjacent, but not too far. And the Traveline website gives great walking maps.
Those NE buses came from the Traveline Cymru journey planner.
On the Nat Ex bus you have a guaranteed seat, luggage handling and a nice snooze.
Certainly a valid route which the OP may not have thought about.

Even more interesting is that Traveline gives you another way into St David's. It may not be ideal for arrival day, but if you've snoozed on the bus could work. The normal bus to St David's also runs to Fishguard but there is also a very summer scenic bus as well around the coast called the Strumble Shuttle.
If you were on the 0730 National Express from Heathrow you can connect into that scenic bus at Fishguard & Goodwick station.
A fantastic way to arrive into St David's.
Not one which would have cropped up at first or even second thought.
It is a direct train from Newport to Fishguard.

the key thing was that the OP was brief, vague and couldn't make sense of whatever it was -and was then subjected to a wall of suggestions without anyone knowing what didn't make sense