An Oyster card is just a card you buy and load money onto, so it just depends how much you will use it as to wether it is worth paying £5 out for it or just buy the paper travel cards that cost a bit more than an oyster fare.
Wembley Stadium station is for the national network line, the Chiltern rail line runs through it, this is the closest train line only a few minutes walk, to get the Chiltern you will either need to get it from Marleybone in Central London or find the nearest train station to you, it'll depend where you're staying as to whether this is at all feasible. The tube station in Wembley is about 10 minutes away (I thought it was further than this I have to admit, I could have sworn it was 20 mins when I last looked but we live on the Chiltern so it's much easier for us) so that is do-able it looks a simple walk from the search I did (plus there will be crowds of people anyway so I doubt you'll get lost) but I would check what time the last tube is, it'll depend how residential it is, I imagine it won't be as early as the station by the Emirates, that was stupidly early!