My thoughts: If you're new to the system (even if you've played an older edition), don't go changing things around until you see how they work. Seriously. I've been (primarily) GMing for over 20 years, mostly in D&D. And I've played 3.x since it first came out. I've putter with the mechanics quite a bit and, with very few exceptions, have come back to using core rules.
Let me be clear: it's not that there aren't better ways of doing things. It's that there aren't many "simple" solutions that work better. Don't make changes unless you've got a good idea what you're getting into.
Realism is over-rated. No, really. I've even got a nice, thick streak of Simulationist in me, and I can say that. D&D is a large-grain system. It doesn't do "real" very well and cannot be made to do so -- at least not without making it unrecognizable as D&D. If you want something "believable", remember that 90% of combat (and much of other activities) are abstractions. The dice just break things into manageable bits, mechanically. That 16th level fighter really isn't swinging that much faster than he was at 4th level -- he's just gotten more efficient with making feints, etc. potential hits. AoOs aren't just a single prepared shot, they are a combination of the hazards of running through a combat zone and the readiness of a combatant to take a pot-shot here and there.
Just be descriptive. When in doubt, ask what sort of abstraction the rule might represent.
On the topic of minis: I'm starting to like them. I've used dice, etc. for years and years, but the collectable minis are actually kinda nice. And much more affordable. Regardless of whether you use minis or some other marker, I strongly recommend using a battlemat of some sort. Being able to see the layout of combat helps a lot in getting everyone to understand what's happening.