Rusty water is primarily mechanical dirt, and filters actually work for that. But here's the thing: if the pipe is already rusting in the basement, the problem will keep coming back because the source isn't fixed. Still, a faucet filter or an under-sink one makes sense.
For your situation, a combined approach would work. First, install a mechanical coarse filtration filter (mesh or polypropylene cartridge) - it catches the rust itself. Then add a carbon cartridge to get rid of the smell. A lot of people just buy ready-made two-stage under-sink systems - they're not expensive and easy to replace.
The only thing is, you'll have to change the cartridges often. With water this dirty, the mechanical filter will clog in a month or two, maybe faster. So factor in the cost of replacements. And check if maybe your neighbors have already worked something out with the building management about the pipes - sometimes they actually do clean or replace them.