I will wager a guess that you are:
Adam
I was the freest man around.
In his creation story, Adam was the first man on Earth, and was free to do anything except eat from one tree.
Yet I never left my grounds
(for years at a stretch)
Having everything he could want in the Garden of Eden, Adam had no need to go anywhere. However, he was eventually forced to leave after the trick of the serpent.
I could walk, fight, or run.
I'm as able-bodied as anyone!
Again, he was the first man, and made in God's own image, so he was likely able-bodied, even if there were few comparisons available. He was able-bodied enough to have another body, that of Eve, created from his own, but that was probably more of God's work than Adam's.
And my riches I can't count!
God gave man dominion over all other creation, and in Eden, there would be no want, instead plentiful...everything.
But I rarely ventured out.
He didn't leave the garden. Though, when he left Eve's side, the serpent tricked her into eating the forbidden fruit and they were both expelled from the garden.
I'm stable mentally and emotionally
He wasn't crazy, he just became more aware after eating the fruit. Like seeing he was naked and covering himself, for instance- not crazy.
And many dream of being me.
I am sure many men would dream of being the only man on Earth, in the paradise of the Garden of Eden, made in God's own image, and with an eternal mate. Could be worse.
Also, Related:
https://puzzling.stackexchange.com/a/28998/11452