The Tavern

I have not been playing much lately and I find myself intrigued by centuar and Okra (so you get the barding). What do you consider the best background/strat for actually getting one of these, um, running.

They have an incredible aptitude for ranged weapons, bows/throwing in particular, so a hunter is a great choice. That said if you wanted to go melee just because they have a -1 for weapons doesn't mean they can't make good melee fighters. Unarmed is +0 so that's certainly an option, although you'll waste whatever god weapon gifts you get.

The main downside to centaurs is the -3 armor, -3 dodging, and -3 shields, meaning that getting good defenses is very slow. Using a hunter with bows would save you a lot of exp to dump into armor/dodging, if you go that route.

Chauffeur.

Centaurs are one of the strongest species in Crawl. They combine decent aptitudes (universality) with speed 2 (game-breaking), very high HP, good UC and a good ability to wear shields. Yes, their apt is -3, but they only need 3/9/15 skill to negate buckler/shield/large shield penalties. In addition, they have +3 natural AC. So yes, your defence will usually be under average, but it is far from being actually bad if you play it right (same as a -1 apt is under average but far from being bad), and you have HP and speed 2 to increase your survivability even further. Centaurs don't die easily at all.
I personally would not want to use a bow or crossbow unless I was using using two-handers (and probably I would use UC instead of two-handers, exceptions like CeBe apply). I would either only use melee combat + spells or slings/throwing for physical ranged, for which apts are +1/+3 respectively too.

My personal choice would be CeTm of Okawaru or CeMo of Okawaru. Pick INT in both cases and don't forget to wear a shield. Heroism is very good with UC and very cheap, so spam it. The most useful spell schools are Charms, Translocations and Transmutations. Use Unarmed Combat and keep that at a high level. If you want to fight primarily with no form or Blade Hands, it is definitely worth wearing EV -3 dragon armour. Otherwise it might be preferable to stay in lighter stuff, ie if you want good Statue Form success.

I recently won a CeEE of Vehumet who used Statue Form, Iron Shot and scourge melee combat. I thought it was extremely easy, so if you aren't fixed on Okawaru give this or something similar a try.

I'm a big fan of CeFe, sticky flame and run, run to corridor and make a conj flame party etc. And Conj Flame and Sticky Flame both require little investment to be awesome, and synergize well with melee, adding lots of damage while you hit stuff for only one turn of casting, which lets you can hybridize nicely.