I also work at Gatwick (not the airport) and fly from Redhill (where I trained) and Shoreham. Although Redhill is much closer, I find it only takes a few minutes more to Shoreham due to fast roads.
Shoreham seems to be slightly cheaper, but my club at Redhill includes landing and circuit fees in the rate, which Shoreham do not.
As Evo said, the Shoreham circuit can be VERY busy. This could waste some valuable training time and cause undue stress in the early days. On the positive side, once you can handle it, you can handle any circuit anywhere!
Flying schools run on such tight margins that I doubt a discount will be forthcoming. The co-owner / wife of CFI at Redhill Aviation is (was?) a BA pilot. Might help if that is who you work for?!
Otherwise, the more you pay in advance, the more discount you can get. Remember to research thoroughly before you give ANYONE your hard earned cash.
Feel free to PM me with questions.
TallGuy.