They’ll want whatever medical history you happen to know about the animal, but nobody’s going to jump down your throat for not knowing all the details about a cat you picked up off the street two weeks ago. They will, however, expect you to know how kitty’s been eating and drinking since you’ve had her, how she seems to be feeling, if she’s been vomiting or having diarrhea, that sort of thing.
They won’t be loathe to look at your cat. Seeing sick animals is sort of why we’re there, after all. Since you don’t know about her vaccination status and whether or not she’s positive for FeLV or FIV, though, they might put you in their isolation exam room. Probably not, since those are transmitted through body fluids, but some clinics will do that just to be on the safe side. It would be more likely that they’d want her in the isolation room if she were snotting and sneezing, since upper respiratory infections can spread through the air.
As for costs, that’s really going to depend on where you are. All they can really quote you over the phone is the exam fee and standard stuff like vaccinations, because they can’t know what they’ll need to do until they see what it is they’re dealing with. One thing I’ll warn you about, though–what sounds like a cheap deal can actually wind up costing you money if there are lots of little extra charges here and there. Banfield, in particular, has fairly reasonable prices for a lot of their services, until you get all the add-ons totted up. A little restraint charge here, a waste disposal fee there, and all of a sudden it costs more to go there than to have the same stuff done at the emergency clinic. And don’t dismiss places that include the exam fee in with the vaccines. Twenty bucks for a vaccine sounds like a much worse deal than $8, until you figure in the additional office visit fee. Make sure you do your math. Generally, though, the cheapest place to get vaccines is the shelter. As a general thing, though, they don’t do health checks and stuff. Still, it’s worth looking into.
At any rate, most places will do the exam, then give you their recommendations and estimates based on those recommendations. If they don’t give you an estimate automatically, don’t be afraid to ask for one. I’ve never seen a clinic yet that won’t gladly oblige. And no, they’re not going to think you’re a horrible person for being concerned about money. We tend to be a pretty pragmatic lot about the financial side of vet care. We have to be, because if we ignored the bottom line to help all the cuddly critters, we’d be out of business and not be able to help any of them.
Claws don’t phase us a bit. Like Maddy says, we’re used to claws. If they truly are overly long, though, they need to be trimmed. It won’t hinder her defenses to get the tips knocked off, and it will keep her from hurting herself. Cats can lay themselves open with their own claws scratching, sometimes, and excessively long toesies can get caught in carpets, bedding, furniture, etc. and get kitty hung up. A nail trim wouldn’t be a bad idea at all for her.
Good luck with your new kitty!