My "tips" for Conquest would be probably a bit different than what others might suggest. I'm an offline-only guy, so Conquest is a major portion of my "content" - I don't blow through them like a lot of the online guys do. If you're looking to go "no money spent" than I highly recommend patience with these maps.
Before getting into my tips, here is the most basic: read through all the map goals BEFORE starting
This is how I approach Conquest (let me say it again...this is a "maximize offline content" approach, not "get through it easily/quickly" approach:
1. I ALWAYS play at All Star and above. You'll get more XP and better post-game rewards odds. Plus, lower difficulties can get you into VERY bad habits as the CPU throws WAY too many strikes. All Star is the most ratings-balanced difficulty, so you will get much truer outcomes here. If it's too hard for you to the point where you barely win, by all means, drop down. But honestly, really work to get to the point where you're comfortable on AS.
2. Fighting a two-front war is a dicey proposition. Find "chokepoints" where you can stack up the opposing teams from expanding. As long as you keep a sufficient force on that hex (equal or higher number than the opposing force), you should be fine. Hold that point and focus your efforts the other direction. A couple of maps (1st inning - ugh) do not have chokepoints...I concentrate my forces one direction and gain as many hexes as quickly as possible.
3. I always play the "fan stealing" games early-on. They'll allow you to built up your force more quickly.
4. I suggest playing every game where the CPU has a force size greater than 5-ish in a hex; again, especially early-on. Once you hit that "tipping point" where you have overwhelming forces and are just wrapping up, then by all means sim at that point.
5. I like to rotate my starting pitchers, just go 1-5. This not only gives you a little more realism, but it will give you different matchups (breaking-up the monotony a little) and allow you to rack-up some innings with pitchers from other teams.
Remember, the more you play, the more innings you get for Team Affinity. It seems like a mere pittance at first, but it can add up after a while. It's also usually a quick 3000 XP for me for about 10-15 mins. That's NOT a bad ratio at all.