Get the train!
You have a choice between getting the tube/train down to Victoria, London Bridge or Kings Cross, or, as you live in Hampstead, you can get the Watford Junction service, which means driving (or getting the train from South Hampstead) to Harrow and Wealdstone (not far).
Trains to and from Brighton are very frequent, so you could time it to get the Harrow train down and then come back via Victoria pretty much when you choose. Because you will be starting at the beginning or very early in the service you will have no problem getting seats. Because trains are so frequent, the only time the service really gets full is on the Victoria service when you pass through Gatwick, but that won't really affect you.
The train station is pretty central to everything - only a minute or two from the town centre, 5 mins walk from the sea front. You'd probably find it hard pushed to park there anyway, and I would imagine the traffic down would make the journey time a lot longer than an hour and a half!
Vicky