That's really a view perpetuated by D&D. LotR Elves are just better all round than Men. Still, it's your conversion and your game, so it ought to fit your conception.
There's quite a lot of stuff worth reading on Wikipedia about this. The first thing to say is that there are two types of Uruk. The first type were bred by Sauron and unleashed from Mordor in the year 2475 of the Third Age. They supplanted the lesser Orcs (Goblins), whom they often refer to as Snaga (Slave).As to the question of orcs, I go with the theory that they are corrupted elves and the Uruks and goblins are just evolved from the original. The Uruks were experimentally evolved by Saurman. The goblins are orcs that are evolved to survive in deep caves and mines as opposed to the orcs who leave near the surface and have frequent excursions to the surface. Thats just my take on it all.
Saruman bred his own Uruks, which have the same traits as Sauron's Uruks, and had in his service also a number of Half Orcs and Goblin Men, whom Aragorn refers to when discussing the Battle of Helm's Deep with Merry and Pippin. Precisely what they are is unknown, but they are distinct from Saruman's Uruks. More than likely they are the same sort who occupy the Shire later on.
As a side note, the only reference to Saruman's Uruks as 'mixed with men' comes from Treebeard and it is speculative on his part.
To my mind the best representation in D&D is Great Orc (Uruk) = Hobgoblin and Lesser Orc (Snaga) = Goblin. Again, though, it's your conversion, so really it's whatever suits your taste.
Take a look at these:I'll look into Nazgul's conversion.
Thomas' Nazgul
Thomas' Middle Earth Race Conversion