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.
Hmmm, I would look into
cube drafting if you have a collection of Magic cards to draw from already... sounds like it might fill the need. You basically assemble a stack of 360 unique magic cards and draft from that with a bunch of players (giving everyone three sets of 15 cards, then drafting it like you would with actual booster packs). You build decks, then play! It has the feel of "limited" (like going to a draft at the store or whatever) but all the cards are self contained in one collection that everyone drafts from.
It's lots of fun and evens the playing field, kind of like making the 360 card cube itself into it's own confined card game, which can be tweaked/changed as needed. You don't have to worry about who's bringing the best deck when you play because all the cards come from the cube. I've done a cube draft several times now and it's especially great for people who enjoy the game of magic, but don't want keep up with the new sets.
One downside is it can be tough to assemble a fun group of cards if you haven't got a substantial collection to begin with. My friends and I all pitched in cards to make ours a group effort, but that might not always be possible.
If you can put one together, though, it's awesome. Whenever we play magic these days it's usually with the cube (Or the commander format, but that's a different thing entirely).
EDIT:
Smash up might be something else to look into. Each player chooses two 20 card "factions" (robots, zombies, dinosaurs, etc) and mixes them together to form their deck. Not really a lot of fine tuning, but it has aspects of CCGs while keeping everything contained in one box.