companion for an older cat?

Hello, I'm fairly new to cat ownership (though I have always loved cats and my parents did own a couple while I was growing up, and I've helped friends with theirs) and in a couple of weeks we're getting my brother's cat. Wick is an older (13-15 year old) long haired tabby, I think. My brother got her from a family who had owned her for her whole life, and she had lived there with another cat. I don't think the two were related, but they apparently got along fine.
Well, at my brother's place, Wick was alone an awful lot- my brother worked two jobs, and lived alone himself. She didn't seem to like being alone very much, although she didn't have any bad behavioral problems because of it. She has been described as half dog, half cat that got weaned too early. She's friendly, but not cuddly, will put up with just about anything, and she loves feathers.
So. My boyfriend works full time, and I am a full time college student with a very part time job. We'd like to get Wick a companion, so she won't have to be alone so much (I'd stay home all day with her if I could, but college will be college).

All that said, I have a few questions.
Does the age of the companion cat matter? We were thinking not a kitten, but not a really old cat either- more middle aged. Is that right, or does it not matter?
Should we get the companion close to when we get Wick, or should we give her some time to get used to her new surroundings before introducing a new animal?
Will visiting Wick a lot before actually taking her to our place help with the transition?
Is there a specific temperment we should look for in the companion cat?
We're getting the companion at a shelter (there are a few cat-specific, no-kill shelters in my area) where the people working there know all of the cats fairly well. Is it rude/insensitive/not okay to ask for a specific temperment? I have a tendency to want a lot of kitty cuddles so I'd rather get a cat that enjoyed that.

Thanks!

Welcome to TCS! To answer your questions:

1. Does the age of the companion cat matter? We were thinking not a kitten, but not a really old cat either- more middle aged. Is that right, or does it not matter?

Middle aged should be fine.

2. Should we get the companion close to when we get Wick, or should we give her some time to get used to her new surroundings before introducing a new animal?

I don't really know. Instinct says either get them at exactly the same time, and introduce each to the house and then to each other, or get Wick first and give her time to settle in. Don't get her and then get a second cat quickly afterwards, she might feel like she's been 'sprung' on.

3. Will visiting Wick a lot before actually taking her to our place help with the transition?

Yes.

4. Is there a specific temperment we should look for in the companion cat?
We're getting the companion at a shelter (there are a few cat-specific, no-kill shelters in my area) where the people working there know all of the cats fairly well. Is it rude/insensitive/not okay to ask for a specific temperment? I have a tendency to want a lot of kitty cuddles so I'd rather get a cat that enjoyed that.

It should be fine to look for a specific temperment, as both you and Wick have to be happy with the new kitty.

A male with no history of dominance would possibly be a good choice - ex ferals make good companions for pets, but aren't always lap cats (though they can still be affection hounds).

Here are my experiences:

1. Sassy was ~8 years old when we got her PJ as a companion. We were told Sassy was great with other animals of all kinds, people, etc. That wasn't true, at least with PJ. Now, PJ never, ever approached Sassy - she deferred all bossiness to the Sass-master, and PJ never hissed, growled, talked, nothing with Sassy. Sassy, however, once together with PJ, terrorized her. Sassy was rehomed because she also started attacking us. She's much happier by herself.

2. PJ was around 11 when we got her a boyfriend... ... Teddy. Teddy was about 7 years old at the time. Again, we did all the proper introductions, and this time, PJ was hissy/growling/etc. This went on for about 2-3 months, and there's still the occasional swat or hiss when Teddy tries to play and PJ isn't into it. They're not best friends, they tolerate each other. They'll both sit in my lap at the same time (but not touching each other), or on the bed together, but not quite next to each other. But they share everything - toys, beds, food, water, litterboxes - with no problem. And when they're in a good mood, they chase each other around. PJ is now 13, Teddy is now 9.

From other things I've heard, an opposite gender cat might be the best way to go. Teddy was a bit aggressive with PJ (and still can be), but as the resident cat, PJ (and I'm sure your girl too) can handle her own and will put Teddy in his place - just last night, she raised her paw at him (but didn't swat, hiss, or growl), and he stopped chasing her. They communicate well!

thanks to both of you for your responses.

The problem with waiting for Wick to become comfortable and then getting the companion is that I start my third year of college on September 6th. I'm not sure Wick will be totally comfortable by then, and I'd rather get the second cat while I'm still home a lot to keep them company during the settling in. I suppose I could wait until a school holiday, but I think the best one would be thanksgiving and then there's the spending for christmas to worry about...
I guess my point is, would it be feasable to, as mentioned in the first response, get both kitties at once? Or is Wick too old?
I can definitely wait for the second one, I just think it'd be better for everyone involved if it were earlier.

Thanks!

ETA: Oh! and I didn't mention before but in her first home Wick lived with one other cat and three big big dogs. And four people.

In that case it sounds like you should get them both at the same time. The right temperament for the other cat would be whatever is similar to Wick. Most importantly, I would try to get another cat that has lived in a multiple-cat household before and/or seems to like other cats. It does seem like sometimes a female is a good choice for low tension... there are a lot of fight-prone cats in my neighborhood, and the female is the only one who doesn't fight with any of them. She doesn't challenge the males and none of them give her trouble, either.