Is singlespeed an option? The only bit of mine which suffered from the salt was the drivetrain, ss is so much lower maintenance. It’s also a lot of fun.
Rather than cheap and cheerful I’ve gone the other way on my winter bike/commuter though, Chris King hubs and headset, square taper BB, TRP Hylex brakes, basically just chosen the moving parts for reliability and I can’t fault it. I do have the luxury of keeping it in the office at work though, it’s not outside on a rack or anything. I realise it’s the complete opposite of what you asked but I think good bits (mine were all second hand so good doesn’t necessarily mean expensive, eg £200 for a pair of CK R45D hubs on Stans Iron Cross rims) which last is cheaper in the long run than replacing cheap bits all the time.
Having decent seals on anything with bearings means a blast with hosepipe or jetwash is fine, a spray of the chain and that’s it done.