Monster Classes are completely crippled from what I see. You start out greatly underpowered and it's a slow climb to being half-way decent with most creature's insane Level Adjustment. You don't get to multiclass until you finish it, and I see now way you could optimize playing one as there's so little you can do with feats. So is it even worth playing a monster class?
Compared to Player Character Classes, Monster Classes are typically vastly underpowered.
You talk about 'LA', but refer to classes - a 'Monster Class' typically refers to a Savage Progression from Savage Species, where they take a Monster's LA and RHD and add it together and create a class with that many levels where a player taking that class slowly gets the monster's features. But for the purposes of 'playing a monster', there's little difference between a Monster Class/Savage Progression, and taking the stupid LA and RHD.
The exception to this is a few monsters with full casting (angels, mostly) for their level, and a few low-LA creatures or templates that give great stat mods. Even playing those is vastly sub-par.
As the Tier system (a system for documenting the incredible power-gap between optimized classes) shows, there is a huge power disparity in DnD 3.5e. It goes from 'Gods Amongst Men' all the way down to 'Jim the Guy who can Sometimes Hit People With A Sword'. And players are meant to play both, and be the same rough level of power. That just doesn't occur. Most groups solve this with a gentleman's agreement, a less rules more roleplaying, or by playing very simple characters with very low levels of optimization (and still often run into this problem). Usually the DM compensates on one level or another.
But still, it's an acknowledged fact that 3.5e DnD suffers from 'Quadratic Wizards, Linear Fighters', and most Monster Classes are well on the Linear side of that equation, and even worse, since they often can't even compete with a well-built Fighter.
The Tome Project attempted to balance all classes to the Wizard balance standard, resulting in high-powered, almost superheroic PCs. It's my opinion that they didn't go far enough. Their classes, while useful, don't keep up with Wizards etc at higher levels. Their scaling feats, though are a good idea even if again not far enough.
The Tome method for handling monsters is roughly similar to the Pathfinder method (although pathfinder left it remarkably hazy and littered it with warnings). CR is supposed to be how good a monster is, although it's often poorly implemented. A level X PC is supposed to be the same as a CR X monster. And yes, that means that 4 level 10 PCs vs a single CR 10 monster is unfair. Most DnD fights are supposed to be beatdowns that result in victory for the party. Otherwise there'd be too much PC death. The Tome/3.P system simply says CR = Character Level, for monsters'. So if a Gibbering Mouther (or whatever) is CR 4, then you can play it in a level 4 party, and when the party levels up to level 5, you can take a class level. Or advance it to a higher CR, or whatever you want to do.
I've never had problems allowing monsters with the level = CR system. Racial Hit Dice and all. It seems to work fine. Exceptions obviously exist - some monsters in PC hands are going to be way more powerful than normal. Some groups have a very low optimization and weak characters, so the monster will need to be weaker too (and you should lower the CR for monsters they fight, so they don't get wiped). Overall i've never had a problem with it.
Other fixes involve mostly just reworking the monster to fit the power level of the group(often for level 1). This can be a different version of the monster from normal, or just changing the monster in the setting so the player can play it, making Ogres a playable race from level 1 means removing racial HD, most of the stat bonuses, etc. Pathfinder have a Race Creator tool for this, but I found it very unimaginative and easy to create overpowered races. If you're going down this path, just compare it to things of a similar CR/LA in terms of bonuses.
As it Stands, though.
I wouldn't play 99% of monster classes and races. Even the vast majority of templates result in you being left behind or being useless.
The only time i've played monster races or classes in 3.5e DnD, it was in low-optimization groups where my skill at creating powerful characters for the game allowed me to overcome the weakness of the race or class and still have a powerful/interesting character.
There are plenty of level adjustment templates that you can take that are quite good for optimised characters. You just need to be careful with it, as some are very character or campaign specific.
A good examples would be half ogre. If you're building something like a knight, going for lots of Attacks of Opportunity, trips, grapples and disadvantages to opponents within your reach etc. 6 strength, +4 to grapple and 5 ft extra reach will do more for your grappling than +2 BaB would. You lose 2 levels of HP but gain 2 con and 4 natural armour. 60 ft darkvision, while very campaign specific can be extremely useful.
This is what me and my DM did for my Pathfinder games. We took the Improved Monster Page from the SRD on DND Wiki and used that as a very rough character class outline. The result was Grau the Zombie. He takes anything he wants by buying abilities with CR. Every time he levels up, he can take 1 HD for 1/4 (because undead take 4d12 per CR) or 1/2 for 2, and 1 for 4. We also decided that since most monsters can cast spell like abilities that he can gain a spell under the bard progression of any spell in the game (as long as it made sense) as a once a day spell by spending 1/4th CR.
And on top of that we decided to allow myself (under his approval of course) to make abilities and spells for him. It's resulted in a monster of a Character! (Atm he's a Tanky version of Pudge from DOTA with some nasty spells.) He's pretty fun to play, and to be honest his build is really nice. I was planning on writing out the rules for the whole thing as a Mod and put it out for GitPG forums and the Wiki itself.
So yes, if your DM is awesome and will allow for some cool things, you can build something awesome. Though it needs to be understood that this is NOT Balanced! and that it's up to him to help you regulate it and really it's a test of whether or not you can work with your DM.