Yes, any one should be OK. There are two types of axles - bolted on ones and quick release. They're interchangeable, but you need the Q/R skewer to clamp the Q/R wheel. The Q/R axle is 9mm dia with a hole through the centre for the skewer. The bolt on type is 10mm and solid. If your bike has the Q/R type, you might have to files the drop-outs a bit to get the solid axle in.
It never happened to me. Wheel always fits exactly as it should.
Or go down to the tip. There are always loads down there. One time when I wanted a cheap bike as a donor for conversion, I asked the scrap men to look out for one. A couple of days later, there was a knock at the door and the scrap man was standing there with a new looking catalogue bike for £10.
Probably, it depends which one you got. £70 is OK for one with disc brakes and a 1 1/8 steerer.
To help avoid such an issue, after re-fitting the Q/R, place the bike bqck upright, release the Q/R skewer and let the weight of the bike help 'seat' the wheel into the dropouts nd then re-tighten the skewer.
