You can turn on the expansions and most of their content all at once. A few things are mutually-exclusive choices always: map types, ai types (you only ever get two, but they can be from any mix of expansions and base game), and campaign type (it's either defender or conquest). With all expansions on and complex ship types enabled, there are a total of 54 bonus ship classes, so you won't see all of those in any one campaign, either -- usually a max of about 7 on your team with two players, plus whatever the AI is using against you. So there's a lot of replay value there.
In terms of minor factions, ai plots, and just all of the various other capturables and such that come with the expansions, you can turn all those on at once. In terms of the capturables, those are always on by default if each expansion is on. In terms of minor factions and ai plots... probably you want to tailor subsets of that to your tastes. Turning everything on would be a bit overwhelming, I think.
If you're uncertain, you can always demo the expansions, by the way. You get up to three hours of gametime per campaign with them on in demo mode, and you can continue your campaign past the three hour mark if you do wind up getting them.
Strategically, in a vanilla game with all the expansions on (not with the minor factions, I mean), what you mainly gain is a lot more variety per planet, and more various challenges to figure out. Also more variety in possible AI types, bonus ships, etc, obviously. Some of this can affect the game quite notably, in terms of how you value targets and such (for instance, you could take more planets and then rely on a superterminal to try to drive AIP back down some).
In terms of the minor factions, some of them are quite minor in effect, but others are real game-changers. I'd stay away from hybrids until you're further back into things, and fallen spire you could go either way with early in, but it's a big game-within-a-game.