If you're only interested in using Google maps, then downloading the maps for Greater London on Google maps before arriving will be the cheapest method. The map won't include all features (e.g. Google maps will be incapable of proposing bus itineraries) but you'll be able to find any street, place of interest, closest tube station, etc.

There is at least one vending machine selling sim cards (there might even be two or three) in the arrivals hall of T3. There's a shop selling all kinds of sim but I believe that they are on the more expensive side of things. The vending machine has a couple of different packages from different operators. The vending machine is opposite the boots. Once you have left the secure area and join the public area, there's a ramp going down to the tube and the train station. The boots (& the vending machine) are to the right of that ramp if you're standing right in front of it.

Unless you travel to London frequently, chances are that any prepaid card will expire before you visit the UK again.