The underground is certainly doable, no problem. It's also direct to St Pancras. However, with a cheap price comes a consequence! It is a bit of an arduous journey. There are close to 30 stops between Heathrow and St Pancras so the stop-start of the journey is a bit tedious. Also, the Piccadilly line (i.e. the line you need) on a Sunday afternoon gets very packed from Hammersmith into the centre - it's not only a key line running through central London it also connects very tourist-heavy spots in South Kensington, Knightsbridge, Piccadilly Circus, Covent Garden, etc.
If it were me I'd book a car. The traffic at that time of day/week will be okay getting to St Pancras, with the door-to-door journey being about 50 minutes (I live not far from there and have done the journey by car more times than I can remember). It costs a lot more than the tube for sure, but removes some of the hassle and IMHO will make for a more pleasant start to your time in London. There's another thread on it but I'd recommend Addison Lee
www.addlee.com for Heathrow pickups into town. Not the cheapest (total cost will be something like £75) but among the most reliable and a good overall standard of car/driver.