Remember, all CD players will eventually end up with a failed laser or transport, no matter how well built in the first place. For build quality 2nd hand within your budget then the Rotel RCD965BX would hit very close to the top. If you can stretch to a new machine you could get a Denon DCD520AE for around £140 or a DCD720AE for around £170. The 520 may well be sufficient and will likely outlast any 20+ year old machine you could buy on eBay.
One thing is for sure - avoid old NAD CD players. They've never been the most reliable machines, and flakier than most as they get old. Their amps can go on for ever, but their CD players aren't worth the risk. Arcam players like the Alpha 7 etc. might seem attractive but they are also prone to earlier transport failure than many.