The "minus" of taking the tube from LHR to the city is that is can take up till an hour and if it's warm outside you'll still feel like being in california (no air conditioning).. The plus is that it's not expensive. Also if taking the tube when it gets really busy make sure you stay close to your bags, there aren't any real bag storeage areas. If you are looking for comfort take the Heathrow Express train, these leave every 15 minutes and only take 15 minutes (20 from Terminal 4). These are (compaired to other UK trains very modern), have air conditioned cars and take you right into Paddington station. The price is 11 pounds for a single ticket if bought in advance at the ticket desk or 12 pounds if bought on the train (payable in cash or credit card). Yes, that is rediculous for only 15 minutes.....

Usually the British Airways Visitor Desk will have free vouchers offering 2 for 1 prices on the train tickets, you don't even have to be flying BA to use this offer...

Hope this helps a little

Scott