I think if you're going to rely on public transport then Thorpe is your only option really. Alton Towers really is off the beaten track and difficult to get to using only public transport. However Thorpe Park is serviced by bus, especially if you get a train to Staines train station first, you can get a connecting bus from there that will drop you to the park door. I presume you're flying into Heathrow so you should have no problems getting to Thorpe Park from there.
When are you planning on going? Thorpe Park can get really busy, especially at weekends but also during the week when the schools are off. However it can also be quiet at times. If the park is quiet you'll do everything in a day with time to spare. If the park is busy and you really want to do everything you might need to get a fastpass for a few rides.
But if you get there early, as in before park opening, you could head straight to The Swarm. If the queue is small it's worth queuing for a front seat. As it's the new coaster most people who arrive after you will head there so you can stay one step ahead of them and head for Stealth. Unfortunately they got rid of the single rider queue so it might take you a little longer to get on. But assuming two trains are running you'll be on soon enough. I recommend row two, you get a similar experience as the front row but with much less waiting.
I'd probably head for Nemesis Inferno next as it's closest. I like the back row as it can be quite forceful. A front row ride is worth it too if you don't have to queue too long. After that you just have Colossus and Saw left. Well X:\No Way Out if you want to ride a ridiculous coaster! Saw usually has a long enough queue throughout the day so either wait your turn or possibly buy a fastpass at the queue entrance if time is running out. I find Colossus gets quiet towards the end of the day, about a half hour before the park closes, so you should get a few rides in then. Swarm has pretty good throughput so you could probably return a few times during the day and get on without too much waiting.
As for the flats I'd recommend Slammer, Rush and Samurai. I usually give the wet rides a miss but if you don't mind getting absolutely soaked have a go on Tidal Wave. The flume ride and Storm Surge are only OK in my opinion.
Thorpe gets a bit of a bad rep at times but it has some great rides. It's my local park so have a bit of a soft spot for it. Hope you have a great day whenever you go.