So to sum up, your options a

- underground to Bayswater, via Earls Court - 50 minutes - £4.00, or
£2.00 if you buy Oyster (which would be a wise thing to do, unless you
don't use public transport), which costs £3, but it can be refunded
when you leave UK.
- train to Paddington - then you can either walk, or take a bus or go
by underground.
- Heathrow Express - 15 minutes - £14.50
- Heathrow Connect to Paddington (runs every 30 minutes) - 25
minutes - £6.90.