I have a parts gun mauser with a chinese receiver. I don't know if any of the other parts are original to the gun. My dad and I are working on it trying to clean up the bolt and make it shoot. It has a J.C. Higgins model 50 30-06 barrel on it (which is probably worth more than the entire rifle).

Here's my question: With the bolt closed on an empty chamber there is a little forward and backward wiggle. With the bolt closed on a loaded cartridge, it is tight.

I don not want to fire the gun until I know what is going on here. I don't have a set of go/no go gauges for it.

Is this forward/backward bolt wiggle bad? I checked my other mausers and none of them exhibit this.

That wiggle is the difference between the rear safety lug on the action and the front locking lugs. Or the face of the barrel to the bolt.
Either way as long as it headspace correctly it should be fine. But not knowing how much wiggle is there I would say check it.
I would reason to guess that since the bolt is tight with a cartridge I would say it's ok but you would not know for sure unless you headspaced it.

Gauges are cheep and a 30-06 gage will do more the a few calibers so it would be something I would buy just to have on hand.

dpcd

I mainly bought it for the barrel. My thinking was to get a receiver that I would not be afraid to screw up. I have an FN Columbian action that is smooth as glass and I do not want to ruin it "experimenting".

What do you call a Chinese mauser? I used a Brno with the Chinese flower symbol on it. Is this a Chinese mauser?
Butch

It's a chinese copy of a German mauser. They were made in China during WW2. Also called a "Chiang Kai Shek" rifle.

Ball's book on Mausers has a section on the Chinese variations- Mukden Arsenal, Chang Kai Sheks, fakes, etc. I'd look there to get an idea of their reliability.