Firstly, what level of game do you want to see? The Premier League will always be challenging to get tickets for, especially in London. Memberships are a possible route but that can still be difficult, even harder if you want tickets together. Hospitality can be a way to get round this, but at a significant or even astonishing price.
However, if you’re happy to look at the EFL Championship or Leagues 1 and 2, you should be able to get tickets at will and even by walking up at the games.
I assume that you know that games can be moved for live TV coverage? Any plans need to take changes into account. Games are currently fixed up until the end of February. Also bear in mind that there is an international break at end of March which often clashes with Spring Break for US visitors.