You do realise your next to asking for a whole list here, right? lol
Diamond is so far the only one I really dislike. So far.
Some of my favourites are:
Garnet - it's really a group with several species.
But most of them are easy to cut and polish into gems, even for a beginner.
Corundum - Ruby and sapphire.
Very hard, but a pleasure to work with. Sadly, the rough is getting quite expensive.
Precious Opal - Very variable and good looking rock. A (fun) challenge to orient the rough correctly.
Aussie opal still tops it, IMO, although I know many like the Ethiopian stuff.
Tourmaline - Comes in just about all colours.