Assumption: you'll be out of the terminal at 14:30.
Choice one: Piccadilly line to King's Cross St Pancras - takes just over an hour. Oops, you've missed the 15:15 from KGX, so it will be the 16:15 which involves two changes (the train doesn't stop at Grantham, so you need to change at Peterborough for one that does) and arrives Nottingham 18:22.
Cost - £28 if bought now, 'only two tickets left at this price'. £55 on the day. Both plus the £6ish cash fare from Heathrow or the more sensible Oyster deposit plus Oyster fare.
Choice two: coach from Heathrow. Dep 15:30, arr 19:10. Cost £18 if booked now, £45-£47 on the day.
There's no contest! Book the later coach, paying an extra £5 for the flexible fare: "It allows you to get on any available coach 12 hours before or 12 hours after your original coach departure time. You can also amend your ticket free of charge to a new departure date. So if your flight is delayed, then there’s no need to panic, you can just hop on the next available coach. It also entitles you to refund your ticket free of charge up to 24 hours before departure".