While the Gatwick Express is good, you may wish to consider take the Southern line. It takes only from 0-15 minutes more (depending on which train you get), but costs £10 per person less. The GE will cost around $18, while the Southern line costs £9.25 (or £9.75) per person. It will make between 0 and 2 stops before Gatwick airport. It also runs just as often as the GE. You can check it at www.nationalrail.co.uk, using the Journey Planner and putting in London Victoria to Gatwick airport.
There are many hotels within a three to four block radius of Victoria Station. Many are good, but many are known to be, shall we say, not the cleanest. October is becoming a bit busy, so you may wish to do some checking now. If I can help in any way, feel free to throw some names out there either here or in a private message, and I'll be happy to let you know what I know about any of them.
London's easy to get around, as transportation is excellent. Expensive, but excellent :-) Staying in this area (Victoria) means you'll be able to get to the Station for your train in an easy 5-10 minutes' walk.