Transportation options in london?

I'll be a tourist staying in zone 2 for 1 week. I have an international student card. If I want to see the main attractions like Big Ben, London Bridge, Westminster Abbey, Buckingham, etc-what is my best transportation option? Could I walk half the time and buy single fares or should I get 'travel card' or 'oyster'? There are many options in London. Please clarify my cheapest, most efficient options. Thanks!