A few thoughts from someone who lives in London at the moment. With the disclaimer that I don't look into this much...
If you're only making a few trips, an Oyster card will pay for itself after about 2 of them or something silly.
If you're doing a lot of travelling in a week or two, it might be worth adding a Travelcard to said Oyster card (essentially making all tube journeys within the zones of your choice, and
all bus journeys in all zones free). There are student discounts on travelcards, but you have to apply for a different student oystercard and provide proof that you're based in London or somesuch, so it would probably be difficult to sort out
.
http://www.tfl.gov.uk/tickets/14416.aspx <- Far too many prices to pick from.
