Contactless is the way to go IMHO. Why don’t you want to use a credit card? Afraid of losing it? In that case, use your Apple Wallet (assuming you have an iPhone) and just tap in and out on the tube using your phone.
I admit that can be daunting the first time if you have never done it… but once you do it the first time you will be off and running.
An Oyster card is seven quid, non-refundable. I don’t recommend it.
EDIT: okay, y’all make fair points about quibbling over seven quid for an Oyster card. :-)
Also: I am on Team Bus! isn31c makes an excellent point. The bus is dirt cheap, and you get to sightsee as you travel between Point A and Point B. Since I moved to Chelsea/Fulham I have basically not taken the tube at all (unless going a distance, like to Liverpool Street or Whitechapel) and so I am unclear on why I forgot to mention how great that option is.