Axiom owners are a happy bunch. The Internet direct model works well for a lot of people...they get to try the speakers in their own home, and if they like 'em, they keep 'em. Otherwise they send them back.
I do take reviews with a grain of salt though, as it is only YOUR ears that can decide if they are really good as they say. I've heard Axiom speakers in the past and I can't say they make me want to pull out my wallet, and I prefer to audition and deal with a local dealer. I believe you can beat Axiom's sound and value for the dollar by careful shopping with non-Internet brands.
So, if you want to go Axiom, by all means give them a try, you may find happiness, or you may be out a bit of money in freight costs in sending them back. Either way, you'll be one step further toward the right system for you.
As for knowing what good sound is.....it's a bit of experience, trusting your ears and instinct, and knowing what to listen for. Also, comparing speakers side-by-side can also be revealing.