FWIW, I'm headed to London next month for five days with some friends and will also stay at the Sheraton Park Lane - if only for its great location. If you don't want to deal with getting the highly-recommended Oyster Card upon arrival at LGW (when sleepy after the overnight flight) I'd suggest ordering the the Visitor card online in advance. They mail it to you so you'll have it in your pocket when you reach Victoria Station (see the earlier mention that the Gatwick Express trains are not on the oyster system, but just about everything else you'd possibly want is: Tube, bus etc.). I just received mine in the mail last week. The good thing about the Oyster Card is it has a daily cap on fares - once you reach that cap you're no longer charged. This can be a real savings if you're running around to/from tourist spots for four days.
http://visitorshop.tfl.gov.uk/tfl/lo...r-oyster-card/