It's great that you are going for a rescue hamster, this is brilliant because they can give you a breakdown of their personality.
They should be giving information such as 'friendly - great first time hamster', or 'needs an experienced handler' - usually means they are a biter. But deffo ask the questions and usually with any decent rescue they'll be giving you a break down before you take a hamster home.
For a first time hamster you want one that is well and friendly. Their home is really important as already pointed out. I have different homes based on my hamsters personalities - I have an older gentleman with me who gets on brilliantly in the Imac fantasy. Overall it's probably my favourite home. You need extensions though and when you start adding them it gets expensive - without extensions it's not nearly big enough. You need atleast two or three for a healthy well syrian, some people go up to five extensions! You can find these homes easily enough on ebay though and pick up some bargins from people who already have one or two extensions - making it cheap to just pay for an additional one or two, depending on what you source.
I also have the savic metro heaven - which is ok. It's the right size, I think it would be better with different levels. If they ever made something which was a cross between the savic for it's floor space and the imac for it's levels - I'd be out to buy it pronto!
I also have the phoenix which is beautiful but my Princess is having a hard time navigating around it. I've just bought a host of supplies to make her home friendly - went to the post office and bought lots of boxes and tunnels etc. She keeps jumping off high things! She's pretty hardy and a little daredevil but I fear one day she may just land badly so I'm going all out to prevent that. She does seem to love her home and can build up some speed running around in it.
Whatever cage you get though, remember they have to spend their whole life in it. So imagine that you are laying on for them a brilliant mansion! If you had to spend all day everyday in one place - you'd rather live in a spacious home with loads to do then a cupboard.....
But whatever you do, do not get a rotastack or anything similar - they are dreadful, hard to clean, hard to put together, hard to put back together every time you clean (imagine if it takes you five hours to put it together the first time, it's going to take you 2.5 hours to take it apart and put it back together even when you truly have the hang of it. Plus they generally just fall apart - they are cheap plastic rubbish!), they are way way too small, and it's impossible to interact with your hamster, such as giving them treats through the bars and talking to them, it's difficult to take them out, and the ventilation is terrible. So just don't go down the plastic tubing system. I learnt the hard way and paid the price too.
Also you need a good wheel - the Karlie wooden wonderwheel is sooooo quiet and big enough - think it's the large - but double check because can't remember if it was the large or extra large that they make for rats - it's basically the one below the one they make for rats. FYI it doesn't properly fit in the imac and I've needed to make some adjustments to get it in. The savic 8 inch though fits fine but it's noisy - you can sort this with a bit of vegetable oil but you have to keep doing it!
Also a good question to ask is what kind of clock does the hamster your interested in keep. Princess wakes up at 4pm - this is brilliant because I have all evening to play with her. She goes back to bed around 2pm. Prince Philip will get up for a drink and a mooch around lunch time but is no mood to play, but then gets up around 1am where he gives a chew on the bars to let me know he wants to come out, once he's out and had his fill he won't chew the bars for another 24 hours until he wants to come out again - it's soooo cute! JC will try to hold out getting up till the house is completely quiet! He's a light sleeper though so every time I go in the kitchen his nose is at the door waiting for treat, but he won't come out for ball time until atleast 11pm. He's lovely for having a mid-afternoon chat with though, I can sit down next to his cage and he'll have a nosy and give me hammie kisses through the bars. He is really friendly he's just super territorial and very nervy with movement, I fear he could bite if handled in a way he didn't like.
You need to make sure a hamster fits in with your lifestyle, because hamsters need ball and explore time every single day, unless like my JC they just point blank refuse to come out on some nights. But you'll need to invest atleast 30 minutes a day playing with them. I usually do 20 minutes in the ball and 20 minutes out with me playing on the bed, or in their make-shift hamster playground. Basically use boxes etc, hide treats, use a maze and toilet roll for them to run round and explore.
I'm a nightowl so that's why hamsters are a perfect pet for me.
Hope all this helps, so pleased you are going to a rescue, so much better than a petshop where you really don't know what type of personality the little one might have when you get them home. My brother got his son a hamster from a petshop and he's a biter! My poor nephew can't do anything with him, he's drawn blood with everyone for absolutely no reason. It's a shame he didn't think about going to a rescue, he just thought ok my son is now old enough for us all to enjoy a family pet and went to the petshop to get a hamster......I've offered to take him, I can live with a biter but as my brother is the honourable sort, he's said, nope he's our hamster good or bad we got to keep him and look after him because that's what they're trying to teach my nephew and I can only commend him for that really. We shall see how long it lasts though!
Sorry I'm a hamster lunatic and can talk about hammie's all day long. Any other questions go for it!

xxxx