I have rarely gone looking - I got Tig by default as she was the only one in the rescue, wasn't quite what I was looking for, as I was swaying towards oldies then, and she was 5 - I thought she would be the cat that I had for years while oldies came and went, but Ginger ended up being that, as she only had 8 months with me - only cat I have adopted under the age of 10. Snowy came accidentally, I wasn't going to get a second cat after Tig, but somethign made my friend take me to a rescue on teh way home, I was adamant I Wasn't going to look at the cats, but couldnt do it!! My friend picked Snowy though, as she was the ugliest oldie!! The only other cat to have come from a rescue (other than failed fosters of course!!) is Mabel, I was told the rescue didn't have any oldies, but was invited to go and see them anyway, and there was a clearly old cat in front of the fire, so I asked about her and was allowed her - despite teh fact she was only here for 5 weeks, I am glad I did.
As I foster, it is rare that I have to go and adopt a cat, and my only criteria is that they are 12+, tends to narrow things down dramatically!! I do prefer one male and one female, but since Ginger died, I have only had females. Not too fussy on colour, except I would prefer not to have a tortie.