Short answer: clean, complete, and undamaged. A chip or crack in glass or ceramic isn't just a cosmetic issue — it's usually a straight refusal, since a chipped item can't be safely resold.
Broken glass and ceramics generally can't go in standard household recycling — check your council's guidance, as many require these to go in general waste or a specific glass collection point rather than the usual recycling bin.
Check the shops currently accepting bric-a-brac near you before you pack the box.