I would say working out a NG paladin variant with your DM is probably the best option, but if you want to go with strictly RAW classes your best core class option is cleric. As long as you're up for tangling with Vancian magic rules, a cleric can be an even better tanky-style fighter than a paladin thanks to the great buff spells they get, and if you take the Destruction domain you even get a smite ability. You don't get a mount, but frankly for a typical D&D game using a mount is kind of a mixed bag unless you're a halfling or other small character. Warhorses don't do so hot in dungeons.
If you are set on having a mount, you can just buy one (the PHB lists prices for warhorses and the like, and if you want something more exotic that can probably be worked out with the DM), or better yet take this feat:
Random Encounters: Wild Life - Animal Companions for Any Character
Invest some skill points in handle animal, train it for riding, and there ya go.
Outside of core, the favored soul from Complete Divine would work similar to the cleric while greatly simplifying your magic use -- it works like a divine sorcerer, a bit closer to a mana system than traditional Vancian. You'd draw from the same spell list as the cleric, giving you access to all those same great buff spells, and you even get better saves and some elemental resistances that would make you a bit tankier. The one downside compared to cleric is that you don't get heavy armor proficiency, but if you take the feat you can still wear heavy armor without penalty, or if you save up your gold you can just get mithril full plate.
The crusader from Tome of Battle is also a very good option. Your saves wouldn't be quite as good, which makes you less resilient magic effects, but the steely resolve class feature lets you withstand hp damage better (especially if you combine it with the Stone Power feat from that same book) and at higher levels you gain mettle, which is a god-tier ability for a character that's supposed to be really tough (and one that paladins don't get, though you could get it through PrCs). The caveat with crusader is that you're reliant on martial maneuvers, which are in many ways similar to spells. Generally speaking, I'd say maneuvers are simpler to work with than spells, but they're still definitely more complicated than the standard non-caster classes, and the crusader's maneuver system is by far the most complicated of the three martial adept classes. Personally, I rather like the martial adept classes, but I understand they're not everyone's cup of tea.
You might also consider fighter going into a paladin-esque prestige class, such as Pious Templar (Complete Divine; gives smite, paladin spells -- which means you can use wands of CLW, letting you serve as backup healer -- DR, and mettle) or Hellreaver (Fiendish Codex II; gives smite-esque ability, self healing -- though unfortunately no ability to heal others -- and mettle, among other nifty abilities).
