Probably best to go Half-Orc with maximum Strength, of course....
There's probably a prestige class or something from Complete Warrior that would help, but I dunno..... Was Drunken Master reprinted there? It's a monk-appropriate PrC from Sword & Fist, and it's 7th-level ability 'Drunken Embrace' gives +4 on all opposed grapple checks.
Relevant feats from Oriental Adventures (just summing these up):
Choke Hold
Prereqs: Improved Unarmed Strike, Improved Grapple, Stunning Fist
If you maintain a pin for at least 1 full round, you render the opponent unconscious for 1d3 rounds if they fail a Fortitude save.
Earth's Embrace
Prereqs: IUS, IG, Str 15
You do critical unarmed damage each round you maintain a pin.
Also, take Clever Wrestling from Masters of the Wild (I think it was reprinted in Complete Warrior or something, wasn't it?), which requires IUS and Small or Medium size (gives a bonus to grapple checks for escaping a grapple or pin, against larger foes), just in case you need to get out of a grapple with a big nasty monster that you don't stand much chance of beating in a straight grappling-match.
Close-Quarters Fighting is also a handy defensive anti-grappling feat, since you have to recognize that no humanoid is going to be wrestling ancient dragons and frost giants very well and needs to avoid getting stuck in their clutches. It comes from Sword & Fist and I think it was reprinted in Complete Warrior or something; prereq is just a BAB of +3, and it allows you to make an AoO any time someone would try grappling you, as well as adding the damage you deal on that AoO to your opposed grapple check to avoid becoming grappled.
I'd suggest 4 levels of Fighter before becoming a Monk, though, to get WF and WS for the unarmed strike (in the meantime you can play at being a greatsword-wielding, well-armored maniac). Also, at some point take Superior Unarmed Strike (from the Tome of Battle: Book of Nine Swords); it's a feat that gives you some better unarmed damage, and if you are a Monk, it instead treats your effective Monk level as 4 higher for purposes of determining unarmed damage.
Heck, while you're at it, you could take the Martial Stance and Martial Maneuver feats once (they're Fighter bonus feat options, too, IIRC), and pick a useful 1st-level stance and 1st-level maneuver from the Tome of Battle. I think there's a Stone Dragon stance or maneuver at 1st-level that helps with grappling, but I can't remember for sure off the top of my head.
At the very least you could gain Burning Blade or something, right? With monkish flurry of blows, you could be getting fairly decent use out of Burning Blade, even though it would only be once per encounter from the Martial Maneuver feat.