Lydd is the furthest from EGMC, Manston and Biggin probably about the same distance - but Biggin has absurd amounts of traffic sometimes, and you could spend a large part of your time sitting on the ground waiting to get airborne.
I'd suggest Lydd - further, and more interesting things to see on the way.
Flying time will depend on the aircraft you use, whether you go direct or via somewhere, and the wind.
Direct, no wind, I'd expect a 150 or 152 to take about 20 minutes to Biggin and Manston, and about 25 minutes to Lydd.
But hey - why do you wait for birthdays and trial lessons? If you work at it, you can get to know a lot of friendly people at EGMC who will offer you "spare seats" when they are flying somewhere. I've taken folks to the Channel Islands before now, when I've had an empty seat. OK, you can't log it as official training time, but you may well get to pole it anyway.
For example, there's a PPRuNe fly-in at Sywell soon (look at the top of Private Flying), and I've got at least two empty seats in G-UTSY going there.
Speak to the Kentish Fledgling - he's done a fair bit of flying in his time...