Heathrow Express is very comfortable and quick, and a bargain at £5.50 - for somebody who wants to go between Paddington and T2/3/5! But you don't.
With its easy, cross-platform change, it would take a lot to persuade me away from the Tube for your journey. Taxi only if the tubes are disripted, or you really can't face it on the morning of departure.
You can get fare estimates for Uber on Google Maps Directions - at least I do on my mobile version. And black cab prices
here.