I know there are better armors to find out there, especially Havel's, but what should I keep in mind with getting his (and in between) stuff?
The keys to playing a heavy in Dark Souls 1 are your shield, your weapon, sufficient Poise from your armor, and your health.
-You want a shield with extremely high stability to block attacks while using the least stamina possible. In practice, this means Greatshields (and thus a high STR stat to properly use them). But you can get by with highly upgraded Medium Shields like, say, a Black Knight Shield. You probably won't have the Titanite (or Embers) for these in the early-mid game, however. The Grass Crest Shield probably won't cut it as far as blocking goes. Too little stability. You want either a Havel's Greatshield or one of the Artorias Greatshields towards the endgame.
-You need a weapon that can deal a lot of poise damage so that when you hit enemies after blocking, it stunlocks them. The heavier the weapon, the more poise damage, generally speaking. Greatswords, greataxes, large clubs, and whatnot are all great. The Drake Sword is a little weak, and will become moreso as you advance through areas. Grab the Claymore off the Hellkite Drake's bridge, or go buy a Bastard Sword from Andre. Again, you're going to want Strength to wield these.
-Stack as much Poise as possible. Higher Poise means you can take more abuse from enemies before going into a hit-confirmation animation. Stone Armor is good, but if you need extra Poise without a lot of extra weight, explore the Darkroot Garden carefully for the Wolf Ring. Tons of Poise for the cost of one ring slot.
-Have sufficient health. You need to be able to not be one-shotted by enemies, so you can take advantage of your poise to chug Estus Flasks while in combat without fear of being interrupted during the animation. Also, upgrade your Estus Flask with Fire Keeper Souls (at, ironically enough, Fire Keepers) posthaste to recieve a larger healing boost with each flask use. Consider kindling bonfires to increase Estus Flask numbers at each rest to 10 (or up to15 or 20 with the Rite of Kindling).
So your idea as a heavy is to stack poise, carry a good shield, block enemy attacks, and punish with an extremely damaging strike that will stun the enemy. Sufficient stamina and weapon power will allow for stunlocks and make the enemy powerless to stop you from beating it to a pulp. Tougher foes, like bosses, might require some healing. Poise will allow you to eat their attacks without flinching, if need be, giving ample opportunity to chug Estus.
You can amp up this strategy even more with things like the Pyromancy (magic available to virtually all builds) Iron Flesh. Just don't plan on dodging out of the way.
This playstyle is decent enough at PvE in the lower rungs, but will quickly become obsolete at higher New Game+ cycles. That's probably okay, however, because New Game+ sucks in DkS1.
However, don't expect to win any PvP matches...you'll be backstabbed after practically every attack, if the opponent is halfway competent.
And how useful is his ring for that? I know he drops a neat ring but given that he can easily one-shot me I'm putting off our fight until I can at least damage him.
Grants a huge increase to equip burden, making all that heavy stuff you need to bear a bit less of a drag.
If you want to kill Havel easily, grab a Reinforced Club from the merchant in the Undead Burg, strip naked, and slap some Gold Pine Resin on it. Roll behind Havel whenever he attacks and then backstab him. The lightning will pierce through his armor, dealing a good amount of damage. If you know what you are doing, you can also get in a free light attack as enemies recover from the backstab animation (yes, backstabs are completely busted). Do this and you'll expediate the process.
I recommended the Reinforced Club because of the bleed effect. If you do a decent job of landing attacks on Havel in a timely manner, Bleed will build up and he'll take massive damage that is ignored by his armor.