It depends whereabouts in east london you live, and whether it's easier for you to get to Stratford or Liverpool street. Overground from Liverpool Street to Colchester will cost around about £15 - £20 return, but this will massively vary depending on what time of day you go, how far in advance you book it etc. Also, get a young person's railcard as that will help loads. Depending on what you are going to be studying, you're probably not going to have to be at uni every day so commuting would not end up being too expensive, in comparison to accommodation costs at least (this isn't reason enough to make the decision to commute though). Colchester is quite a bit further out than zone 6!
It's up to you whether you want to live on campus or not. Essex is quite a 'local' uni, so if you do decide to commute you certainly won't be alone. What would be your reasons for doing so?
Edit: Also remember you will need to get a bus once you get to Colchester - it's not walkable to the uni. The bus meanders its way through the town centre and can take around half an hour to get to campus, even more. So if you have a 9am lecture, this will involve waking up very, very early.