I basically want to be able to build a themed deck like you'd have in Magic, or the old LOTR CCG or numerous others. Sliver decks, elf decks, etc. But I'd like for it to happen during or between games and have it all remain a self-contained game in the end. This way non-CCG players get a game they don't have to "study" or spend money on, and can simply drop physically and mentally when game night's over.
The Star Wars LCG has a style of deckbuilding that seems great for this (sets of cards that go together, so you'd choose 10 sets of 6 cards instead of choosing 60 individual cards, making it easier and faster to build to a theme). That game, however, is like "here's your deck, friend, now you take that home and buy more stuff for it and study it like any other TCG". I can't really enjoy it so much because I have to get people to commit, instead of rotating it with the other board games.