This was probably a Martini Cadet rifle, built as an Australian training rifle and originally chambered for the .310 Cadet cartridge, which was similar to, but not interchangeable with, the .32-20 in ballistics. A lot of these were re-chambered to .32-20 when they were imported, but the .310 Cadet round uses a heeled bullet of approximately .321 diameter instead of the .32-20's .312 diameter, which means the .32-20 round leaves a bit to be desired in the accuracy department if the rifle still has the original barrel. You'll be able to tell by looking for the "Commonwealth of Australia" roll mark on the right side of the receiver.
A smaller number of these were re-chambered for the .32 Winchester, which does use a .321 diameter bullet, but the twist rates are not optimal for the much longer and heavier bullet. Plus, the rifle generally weighs only about 5 pounds, which means it come back quite smartly when the .32 Winchester round is discharged. In addition, the firing pin hole in the breech face is quite large and you sometimes get primer flow into the hole, which locks the action up.
If the rifle is chambered for the .32-20, you can have it bored to .357 Magnum or .357 Maximum, both of which will work quite well in the action.
If this was originally a rimfire converted to centerfire, you'll need to check the quality of the work, as it ranges from spectacular to abysmal, depending on who did it.
The Cadet action lends itself to customization and makes up into a nice varmint rifle in a host of different centerfire calibers. I own a number of Cadets which have been customized, ranging from a .20 Tactical up to the .219 Zipper, and I have a custom action that will eventually be built into either a .30-30 or a 7x30 Waters for Pennsylvania whitetail hunting. If you go with a rimless cartridge, you'll need to replace the extractor with one that handles rimless cartridges. Bob Snapp's design seems to be the preferred version. I can confirm from firsthand experience that it works quite well.
The price seems fair for the rifle in the condition you describe, at least in my experience.
Good luck with it.