I found out that the Heathrow Connect is 10.20 pounds Paddington to Heathrow. Return (aka round trip) is 20.40. This is still fast but with several more stops. Heathrow Express to Paddington is 22 pounds one way. Booking in advance and round trip may cost less. These two trains have different web sites.
Booking well in advance is the way to go if you want the Heathrow Express. The cost is as low as £5.50 one way if you buy 90 days in advance for travel on a weekend or bank holiday.
https://www.heathrowexpress.com/tickets-deals/prices-fares
There are also discounts on return tickets for couples (the DuoSaver) and also for single traveler ( summer special).
https://www.heathrowexpress.com/tickets-deals/discounts-deals
The Heathrow Connect may be a good option for passengers arriving at Terminals 2 and 3, but it is very inconvenient for Terminal 4 and 5 passengers (T5 includes most British Airways flights) The Heathrow Connect only stops at Heathrow Central, which is by T2 and 3. To get there from T4 or T5, you have to use the Heathrow Express transfer service (free), which adds time ( and hassle) to your journey.
https://www.heathrowconnect.com/station-information/heathrow-airport
Depending on where you are staying, you can take the Piccadilly line from Heathrow into London, maybe even without changing lines. And you can get on at T5, T4 or T2-3. You can also buy your Oyster Card at the Heathrow stations.
This summer I stayed in the Holborn area. I compared the options and found that going directly between Heathrow and the Holborn stop on the Tube was the fastest, easiest and cheapest way to go.
This map should help.
I have taken all three of the options discussed: Express, Connect, Tube. If I can think things out ahead of time and purchase a ticket in advance online plus return, excellent. This time around, I did not have things that well planned. On arrival at T5, I winged it. I added money to my Oyster and then headed to the Express. My hotel was close to Paddington. Because the Connect arrived right in T5, I opted for it this time, though the Connect is not too terribly inconvenient, IMO. I bought a one way ticket because I was not certain of my return. I decided not to stress on any missed savings. As it turns out, I returned via tube in two days using my Oyster. Made me feel I had economized :-)