Given the condition of the bike, you bought a project. I buy projects all the time, I enjoy working on them. But projects are best suited for someone with the tools/aptitude/time/access to parts to do the work.

Cables are just the tip of the iceberg. A bike with rusty cables is going to have bearings and grease that need replacement, immediately. That means wheel hubs, bottom bracket, and headset all need disassembled, cleaned, bearings replaced, fresh grease, and reassembly. These tasks all take specialized tools. If you do not do this work now, you run a high risk of damaging bearing surfaces = you will be replacing bb, hubs and headsets (100X the money).

The cables are actually less critical than the bearings. Rusty cables = crappy shifting. Brake cables are more critical as you need to be able to stop quickly. Bad grease/bearings = bearing surfaces will be damaged = serious $$.

I have bought over 300 vintage bikes in the last few years. 100% of the bikes I have bought in project condition like yours needed the bearing work, maybe 10% of those had damage where the bb or hub components had to be replaced (due to former owner neglect). Heck, most of the bikes that appeared to be in better shape needed bearing work.

Hopefully, you have a co-op in your area. Head there now, as they are a treasure. Not only will they loan you tools at little/no cost, but they typically have a volunteer mechanic who can provide advice. The tools to do the work I mentioned above can cost you $100 to $200. Much better to borrow the tools.

I love vintage bikes. But owning a vintage bike is like owning a vintage home or a vintage car. You need to be ready to spend some $$ on maintenance/rehab. And the more of this rehab work you can do yourself, the less it costs (often a lot less).