Druid with Wild Shape for changing into something big (well, as big as you can, so Medium) with Improved Grab and/or Constrict. In Core, the Medium Constrictor Snake fits the bill well enough: 3 HD, both Constrict and Improved Grab. Your feats are Improved Unarmed Strike, Improved Grapple, and Natural Spell. You are a full caster, so you are good, and you can also Grapple, though that's mostly coincidental to your power.
Your grapple check while Wild Shaped is +4 (BAB) +3 (Str) +4 (Imp. Grapple) = +11. It’s not literally the best grapple check available at that level (a barbarian in Rage would probably have +6 (BAB) +6 (Str) +4 (Imp. Grapple) = +16), but Improved Grab and Constrict go a long way to improving it, plus you have very-good spellcasting and an Animal Companion.
If for some reason the 6th-level limit is lifted, brown and polar bears are excellent choices for Core monsters. In water, giant octopus and giant squid are kind of obviously-amazing choices. Out of Core, there are just too many options to go through; look for Improved Grab and/or Constrict, size, and Strength, roughly in that order.
A level of monk isn’t worth it for getting IUS/Imp. Grapple; that just delays your access to Wild Shape, and you aren’t in dire need of more feats: you can get the three you truly want. The better unarmed strike damage does nothing for you while Wild Shaped. The Wisdom bonus to AC does stay, but monk’s belt, wild armor, or a wildling clasp are all better options than a level.
A level of barbarian, on the other hand, is interesting. That could get you Pounce (Lion Spirit Totem, Complete Champion) on top of Rage, which gives you a +2 bonus on Grapple checks (among other things).
But keep in mind that this means losing out on a second use of Wild Shape per day: not a big deal if you can stay shaped, since the 5-hour duration of the 1/day Wild Shape should see you through most issues, but it is a problem if you need to speak somewhere in the middle of your grappling. That one is kind of a judgment call. If I was going to do it, I’d only take it after I got Wild Shape, most likely, as I’d want to get that ASAP, but going barbarian first and then taking druid also works.