Hesitation: Going up steep hill, in idle with AC on

I have a 6-cyclinder 2000 Mazda 626 with about 75k miles.

Lately my car has been having a little stutter/hesitation in certain events.

When I'm going up a steep hill, the car will stutter a little bit, triggering the Check Engine light to flash a few times, then when I lay on the gas a little more, the stuttering goes away.

Also, when the car is idle and the AC is on, the car will stutter, even causing it to register on the RPM meter. It does it a little bit when the AC is off, but when it's on, it does it very noticeably and regularly

I've been told to go get a tune-up, but I feel like I'd like to fix one thing instead of 8 and save a few bucks. I'd like to spare no expense but that isn't an option right now, any ideas?