I suggest looking each up online for rich descriptions. Here's quickies:
-AAC is usually referred to as a "more modern" codec vs. MP3. Many of us would argue that 256kbps AAC > 320kbps MP3 but I wonder if any of us could actually & consistently hear the difference in a blind tests.
-All 3 are somewhat popular compression formats. If you have much of an iTunes library, you probably already have some AAC and MP3s.
-Apple has defaulted to 256kbps AAC (named "iTunes Plus") for iTunes store purchases. This is Apple basically saying that 256kbps is "good enough." Usually whatever Apple endorses around here is considered ideal and often the "one and only proper choice" and all other options are garbage, "99% don't need" and so on. Of course, when Apple shifts it's defaults, we'll shift right with them so take such views with that in mind.
-MP3 is typically more broadly compatible outside of the Apple ecosystem. For example, you might have a car CD player that can play MP3 (on) CDs but it's less likely it will play AAC CDs. This is not a huge issue as Apple pretty heavily dominates the music world but it is something that probably favors MP3 over AAC for broadest compatibility.
My suggestion: take a few of your favorite CDs. Import a couple of favorite songs into iTunes using AAC and MP3 and then listen to the tracks to see if you can hear a difference. If you live with someone or can get a friend to help you, have them play the tracks and take notes of which versions you think sound the best. See if you consistently pick one or the other. Stuff like file sizes and that won't really vary enough to make much difference.
If you can't hear much of a difference, you can avoid letting this particular spec influence your decisions.