If you're staying at Renaissance St Pancras then I'm guessing that money isn't an issue.
If you want to do it quickly and in some comfort, I'd suggest the Heathrow Express to Paddington and then a black cab from the rank. It's probably quicker than getting a black cab or minicab (uber, Addison Lee, etc etc) all the way from Heathrow.
If you want to save a bit of money, but not be stuck on a tube train for over an hour, then the Heathrow Connect is an option, but it only runs every 30 minutes so you could be waiting a while. If money is tight then the Piccadilly Line to Hammersmith then change, or stay on the Piccadilly Line all the way to Kings Cross St Pancras would be the cheapest option.
The tube is easy enough to use, even with luggage, and the tube station at Kings Cross St Pancras has lifts that pretty much take you into the lobby of the hotel.