A decent frame, fork and wheelset are gonna put you well past your $600 budget.

Best to shop the used market. Surly 1x1 is a good frame, you didn't specify frame material preference. A decent SS ready frame is gonna cost you or go with a regular frame and use a SS tensioner of your choice. There a good ones and bad ones.

Gearing - start at 32/16 and go from there. Obviously, it all depends on your typical trails you ride. I've got a rigid 26er with 32x16, one with 34/20 and a 650b with 32/18 gearing. The latter two I ride frequently in the Blue Ridge mountains area. The other is my beach bike when I visit my parents on the coast.

And Crow Bars were my first riser bars, good **** but yeah, a bit dated. You'd best be served with a modern riser bar that's wider, especially when you're honking on the bars outta the saddle, up the hill.