Pre Crisis Superman did meet He Man and could have been comparable in strength, but that was a very different 'He Man' than what was depicted in the cartoon and later Star Comics. The more recent crossovers, He Man was portrayed as powerful enough to fight Superman pretty well, and it was believable that he killed Superman with a sword through the chest, but we don't really have enough info.
There are some decent arguments that Superman is stronger than Thor, and by extension Marvel's Hercules, but there are also reasonable arguments that they are even. Any differential between Superman and Marvel's Hercules would be minimal IMO, as it would be with Thor.
As generally portrayed, I'd put He man somewhere in the Wonder Woman category in both strength and durability. He (and She Ra) have a few upper tier feats, and He Man has good crossover showings, so he could be portrayed as higher, but in general, I'd give Thor, Superman, or Marvel's Hercules a clear and measurable strength advantage, though not an overwhelming one.
That being the case, overall I favor Hercules here, provided he takes the fight seriously from the start. Because he tends to play around a little at first, it could be an upset...
The most recent he man could fare well against Supes, and I think that a reasonable person would view Superman as being the DC version of the ulk, and so superior in brute strenght to both Thor and Herc, as its just the way he is!
His top end would be about same as a raging Hulk....