The class you're looking for is the Dragonfire Adept (Dragon Magic) which provides a very respectable breath weapon (especially at high levels) "spellcasting" and some alternate forms.
You'll want to read the dragonfire adept handbook, but possible invocations involve frightful presence, interesting shapechanging, dispelling at will (which is sometimes better than SR) and all sorts of fun with dragonbreath. To save time, read through the builds here until you find one that fits your intentions.
If you want to be huge and tough:
- Dragonborn Rapotoran Cleric 4/DFA 1/Eldritch Disciple 10/Cleric 5
this provides significant cleric casting which nets you divine power (HD = BAB and a strength boost) and Righteous Might, which is a much better way of going up a size category. If you really want to tell puny mortals to cower, be a half-minotaur (LA +1 Dragon 313) or half-ogre (LA +2 dragon 313), will provide. Or start out as an anthropomorphic huge viper snake and paint your scales gold.
Instead, I'll recommend an alternate route. Since you're playing a high-level game, take cleric for your last levels, and make sure you have resources for divine metamagic and persist spell. Every day, cast divine power with persist spell and use miracle to persist giant size (wu-jen 7, castable without XP cost via miracle), Spell Resistance (It'll not be all that significant, but you'll have it), Spell Turning, Girallon's Blessing (For the claw, claw, claw, claw, rake series), and the other suite of spells. You'll be colossal and dragon-magical without needing to invest levels in a race.
Make sure your cleric has access to the hunger domain, which gives you a bite attack, and the domain spell "bite of the king" which gives you swallow whole. Unfortunately, there are no spells worth the cost that give you a tailslap or wing attacks, but your Claw Claw Claw Claw Rake Bite Swallow Whole attack sequence will simply have to make up for them.
Despite Looking Like a Human, it's Actually still a Dragon
Alternate Form lists what the creature using the ability keeps and loses - notably, you keep HP and special qualities in the new form (although you gain the ability scores of the creature, so the dragon would lose it's racial bonuses to str and con). So you have all your dragon HD, your dragon skills, your dragon mental stats, etc.
If the Dragon already had levels in a class (in 3.5, nothing stops monsters getting levels in classes, even the 'advancement' section is a guideline not a hard and fast rule), it would still have those levels in a class, and could use any class ability it has. The things a dragon gets called out as losing are natural armour, movement modes, size, natural attacks and breath weapon. So spells, skills, hp, are all fine.
But Alternate form doesn't 'turn them into a regular human of the same CR', or something. They are still effectively the same dragon, but without the dragon body. If you want your dragon to lose his hp and dragon spellcasting in human form but gain equivalent class levels, then you'll need to homebrew something for that. I suggest homebrewing an ability called 'Alternate Self' and having it do that, if you want that to happen.
Best Answer
The rule that says that a dragon "is required to devote a level every few years to its dragon 'class,' reflecting the extra Hit Die or level adjustment it gains from aging" is from the Draconomicon section on Dragons as Player Characters (141-4), and, as such, it doesn't apply to a dragon befriended through the feat Dragon Cohort (104 and 138-9). Thus, like any other cohort, a dragon cohort advances as the DM decides it advances. So such a dragon's advancement, for example, could be exclusively by gaining more racial Hit Dice… or could be by taking levels of commoner so that it can be a dragon of the people! (I recommend the DM have this latter choice be extremely rare and suspect that, in all likelihood, the dragon'll probably advance by taking levels of sorcerer.)
Beyond the dragon-only prestige classes in the Draconomicon, undoubtedly a few others exist in Web articles, magazines, and sourcebooks, but only the prestige class dragon ascendant (90-2) is awesomely better than what a typical dragon gets from having levels in some base classes or even, sometimes, its racial Hit Dice, and that prestige class is quite a ways out of reach of a wyrmling, even a red!
If the need arises to advance quickly a dragon's age category, see Is there a way to make a wyrmling dragon become an adult via anything from any book? To summarize, I recommend a friendly necromancer (oxymoron notwithstanding) cast on the dragon the officially licensed 8th-level Sor/Wiz spell hasten the end [necro] (Holy Orders of the Stars 70) and a friendly cleric follow that spell with the 7th-level Clr spell greater restoration [conj] (PH 272).