So! I have a wonderful kitty baby, Peanut Butter. She’s a great cat, cuddly, lots of meowing, but a bit standoffish. Like, she’s okay with new people, and warms up quickly, but there’s a little fear in her. When I first found her at a shelter day at a pet shop, she was behind the glass and super playful and chasing my finger and jumping around. Once I went behind the glass, and looked in at her, she bunched up in the corner and hissed and flipped out. I went over the next few days and just hung out with her, keeping my distance, and eventually she went home with me. After like two days of hiding in her closet while I read and sang to her, she got comfortable and is now basically a great cuddly cat. I recently started some leash training, and she was hesitant at first, but loved being outside - until other people got nearby. Even with my son, who she totally knows and trusts and cuddles inside, made her run for her life when he approached outside, and her heart was pounding from fear.
Because of how my life works, I’m not home as much as I’d like to be, and I feel like she gets lonely. She needs cuddles and active play, and I certainly wouldn’t mind a new furry guy to keep us both company. Recent circumstances means I’ll be home a lot more, so I’ll have time to monitor and acclimate everyone, but I’m worried that Peanut Butter will be aggressive or unhappy or something. I also kinda think she’d love to have a friend to play with and snuggle with when I’m not here.
So - what advice do you have for finding a new cat? Peanut Butter is 3 years old and female. I’m thinking a younger cat? Maybe a kitten? Not sure of gender? Anything you can think of would be helpful, as I descend into crazy cat lady land 
My cats have all hated having new cats join the household. Some have eventually gotten used to it, but none has ever really loved having the company. Mostly, they keep to themselves, unless they both want to cuddle with the same person.
They do get more exercise if there are two, if only because they avoid each other. 
To provide the counterpoint, my cat introductions have usually gone well. I will say that there are a number of factors that influence that and you can’t control all of them.
- Get opposite gender if you can.
- Age. A kitten will almost always be accepted, even if there is some initial shock and horror. If you’d like to try an older cat, then you need to aim more for personality rather than age.
- Personality. Given what you are saying about her personality, you need a mellow cat who won’t scare her too much, but you don’t want a cat that is going to ignore her completely. I’d aim for “good companion” rather than excellent play buddy. Ask the shelter volunteers about cats that fit that bill. You might also observe and look for cats that choose to cuddle up with other cats, rather than hang out by themselves.
I’ve also found that cats usually adapt well to living with each other, though there’s often an initial period of hissing and swatting; and I’ve also found two (or three, or four . . . that’s enough cats, thorny!) to be easier to live with than one, as they can indeed exercise, amuse, and comfort each other.
Since the current cat is female, either another female or a male, IME. Felis domesticus if given the chance naturally lives in groups of females with a tom or two. (Two neutered toms do often get along fine, even if not related, but the chances aren’t quite as good.)
As she’s three, unless she’s been recently living with kittens, I wouldn’t get an extremely young kitten; the hiss and swat stage might be hard on it, and some adult cats will freak out a bit about very small kittens who aren’t their own. But a somewhat older kitten would be fine. If you get an older cat or for that matter an older kitten, go for calm temperament and a cat used to living with other cats.
This you may already know: start if possible with the new kitten/cat shut up in a room in the house that Peanut Butter doesn’t use much. Let them get used to each other’s scent; then let them get together under supervision, but with each still having their own space to retreat to for a while. Make sure you give Peanut Butter lots of attention during this process to try to keep her from worrying that the new cat will supplant her.