cats

I have a 5 year old cat that I adopted 3 years ago, and I'd like to get him a companion but I'm struggling to identify the characteristics I should look for. Can anyone offer advice?

He's a rugged old soul. He loves playing with my 2 year old dog but otherwise just lounges around nearby but not touching - typical Russian Blue. He does try to clean and cuddle the dog, but the pup doesn't understand and runs away. He was actively cuddling with other cats at the shelter when I adopted him so I think he'll do well with a housemate.

I've met a few shelter cats this week but I'm stressing about identifying which would be a good fit. Are male and female both a good bet? Would it be best to get a kitten, an older cat, or somewhere in between? Playful or extremely lazy, or a lap cat?

I know I'll be happy with any choice, so I'm mostly focused on finding a good match for my Russian Blue. Thanks.