I think getting a few card games that have English on the cards would be an excellent idea.
Of course, from a game standpoint, you want to make sure that not being conversant with the language isn't much of a hinderance. You don't want to have to show your hidden cards to get a translation every single turn. To that end, I've come up with a few suggestions off the top of my head, ranked in order from least to most difficult for a non-English speaker to understand. All are good 2 player games, and all but the last one play well with more as well.
Citadels - There are a few role cards with descriptions of their powers on them, and a bunch of building cards, usually with just the title on them, but there are a few buildings which also have special powers listed on them.
San Juan - Each building card has their powers written on them, but there are still only a handful (20-30, IIRC) to deal with. These blurbs are no more than a few words in each case. There are a few public-facing role cards as well, again, nothing more than a few words each.
(Large dividing line between the first two and these two. Tread carefully.)
Agricola - There are a ton of specialty cards, each of which has a description of their power on them. Only a fraction of them are used in any game, so you'll have to play a lot to see them all. (Personal note: I own the German edition, and can vouch for using this game to help learn another language)
1960: The Making of a President - Ton of cards, ton of flavor text, detailed descriptions of the card's power on each one. Certainly not a good choice to start out with, but this would be a good test once you need something more difficult.