Would a younger cat (possibly kitten) or a more mature cat be a better choice in this situation? Please see details.

Maybe get a one-year-old?

Is there a chance you could take your cat to the pound, and let them select their own friend?

I’m with @ibstubro. I tried to introduce a new kitten to a nearly year old female cat. She already believed she was the alpha female. Every day when I got home from work, she would be sitting on the back of the chair next to the door. As soon as the door opened, she would take a swipe at me, the mean b*&#!*(! When I brought in the little kitten, she ignored it. One day I got a call at work from my husband. He was home early, and put down a bowl of milk for the kitten. He said Erica (Cain, because of her superior attitude) walked up behind the kitten and held its head under the milk with her paw.
Years later, I had a year old male cat, and took in a male kitten. Angus was all predator He loved to climb up trees, jump down, and catch a flying bird on the way. He didn’t like to eat them though. He would leave them by the back door for me. The new kitten didn’t like to do anything but lay on my belly with his front paws around my neck, and purr. He was a total pansy about hunting and climbing, and Angus was disgusted, until he found out Shiffer (Brains) liked to eat his catches. After that, they had quite the partnership. Angus hunted, Shiffer Brains ate the kills, and played lap cat to appease the human. One time, I actually spotted them together in the back yard. LOL. Angus was trying to teach Shiffer how to climb trees, and it was going badly. Finally, Angus went to some two by fours leaning against the garage, and had him practicing on those. I think they celebrated when Shiffer made it to the top and back down. LOLUIP!
It really makes sense if your girl can pick out her own friend. I know for certain some shelters accomodate that, but you should call ahead to see if it is okay with yours.
Hopefully your girl doesn’t get insecure and believe you are trying to drop her off.

I’d go for an older teen, or adult neutered male. Your cat won’t pick its own friend at the shelter, it will be scared out of its wits and will not give a whiz about the other cats. Neutered, opposite sex is usually the best choice with cats.
I adopted a 5 yr. old male to go with my 4 yr. old female 2 Decembers ago.

They were friends within days and best friends now.

Just sharing personal experiences here:
My cat, Cyanide, is one year old. He recently moved in with a 3 year old female, and an 11 year old male. At first they were pretty jumpy, but he settled in within a few days. Now they all cuddle on the couch. Usually he and the 3 year old female, but sometimes the older cat joins in.
So, I’d suggest a 1 or 2 year old based on what I’ve seen.

I second getting a one- or two-year-old of the opposite sex.

Re: “other advice on making a choice”...you probably know this, but easing them in is vital. I would put new cat in a room that is not treasured by old cat. Then, have all family members go in several times, so both cats get used to each others’ smell. At some point, old cat will get curious. That’s a better starting point than having old cat completely shocked because you dropped a new kitty in her bed.

If it were me, I would go with a younger kitty, as it would probably adjust to a new home/new ‘sibling’ more easily than an older cat. But I would try to find one with a more laid-back personality so it wouldn’t start picking on the resident cat. And I would do the first introduction with new kitty in a crate, and keep him/her confined to one room for awhile with controlled interactions. And keep new kitty confined when I can’t supervise, till I’m sure they are getting along ok. Good luck finding your new friend, and we want pictures when you do!!

Thanks, all! Based on some other advice we had already decided neutered male. Glad to see that there is confirmation of that idea.

We won’t take her to the shelter to meet with a new kitty for a couple of reasons. One, as already mentioned, she will be too freaked out by the drive and the stimulation of the other animals. I don’t know that she would recognize the place, but would hate to have her think she was being returned. (I have a feeling I’m anthropomorphizing on that last part.) The other reason – also mentioned – is that they need time to adjust to each other. We still have Callie’s safe room and safe box set up, so we’re good there. The adjustment went pretty well with Rishy because of that. (And because he was a seriously laid-back cat.) It was three weeks before we would let them be alone without one of us home because we wanted to be sure they wouldn’t fight.

Again, many thanks for everyone’s ideas and thoughts. Please keep them coming!

Younger or the same age because the other way around won’t work unless cat fights are welcome at your house.