Go to the heathrow express website. You can purchase tics on line. I have never taken the underground, as I prefer the taxis. When DW goes with me, she takes the underground at times.
Depending on the airline you are taking to LHR, once you go through customs, you may need to take the terminal train to get to heathrow express. The express is much easier after the long flight than a local. But, I think you may be on the other side of the city from paddington.
You are staying a decent way out, so plan on some time to get to your tourist destinations.
Be sure to see the war rooms of churchill, near the palace.
for mexican food, try the texas embassy in trafalgar; bbq at bodeans in soho; original hard rock cafe.
london is expensive. Assume that things will cost 1.5 or so more than at home, before the loss you get due to the exchange rate.
Go to Harrods, see the Diana memorial. If you have kids, pick up some harrods bears (they have a collection, and a special bear each year.
The palace has tours at times when the queen is not around. See the guards at St. James, and then the changing of the guards at the palace.
Recently, last month, the plane was not full, but give yourself an extra hour at heathrow on the return just in case, to get through security.
DW enjoyed tours to stonehange and bath and oford.
if you are getting out of town, Kent is a neat place with the cliffs of dover, and good golf.
catch a production in the west end.
London is non-smoking now, which is nice in the pups and restaurants.
pick up a cuban at J. Fox on St. james, where Churchill still has a couple in storage.
Visit Berry Bros. wine store on St. James, which is where the Texas Embassy was when Texas was the Rupublic of Texas, after Mexico and before the US.
enjoy the trip.