CRT monitors are dirt cheap nowadays, but since the minimal size you could probably get is 17", it's going to be rather bulky. Even if it's used, you can get a decent monitor for a great price.
As for the monitor that came with the Performa (which I'm assuming is probably one of the beige Apple monitors), make sure that it uses the standard VGA connector. If not, then you'll need to get a DB-15 to VGA monitor adapter. If your Mac mini uses DVI, then you might need an adapter that switches from VGA to DVI as well (that's assuming that this would even work using two adapters).
Really, your best bet would be to find a decently sized LCD monitor. The 15" and 17" go for really cheap nowadays.