How cheap is cheap? I am a big fan of Logitech's M-series optical wireless mice. Current favorite is the M325, which lists for $30 but can frequently be found on sale for around $20.
If that's not cheap enough, just stick with Logitech and move down the price scale until you find something you're willing to pay for. IMO Logitech makes the best general-use mice.
I suppose the DPI on the cheaper Logitechs may not be high enough for you, but that is an individual judgement call.
Nostalgia isn't what it used to be.