One issue is that almost all wheelsets out there are going to have a different, ~4mm wider spacing between your front fork tips, which would require that the wheel be forced in or that the fork be re-worked by a competent bike mechanic.

But, getting back the OP's request, a rear axle can be purchased for less than $20 and will then simply need to be installed in the rear wheel, again, by a competent bike mechanic.

Any of the mechanical tasks can be performed by a handy person who has the time to find instructionals online for such bike-specific work, but you assume the responsibility for doing the work correctly and safely.
Note that thin "cone wrenches" are needed, but that often the freewheel need not actually be removed in order to replace the rear axle. A couple of cheap cone wrenches could be as low as $10.

But I would carefully judge the condition of the old rear wheel rim before putting any money into it.

What city are you located in? What sort of bike parts and repair facilities are local? Bigger cities usually have bike co-ops where you can buy donated parts cheaply, where tools may be available for public use, and where people can likely show you how to source and install the correct rear axle. It's great experience for anyone who rides a bike imo. Someone helps you out, and perhaps later you go in and help someone else out.