Good for you for getting her to a vet right away. It really is the best way to do it---so you know if there's any problems and can get on them right away instead of waiting until they're symptomatic to find out.
Greys are pretty cool birds. They DO tend to bond to one person, or one sex. And they will decide who they do and who they don't like---and that can often be a permanent decision. They're also very, very timid birds, so treat her gently and do your best not to spook her, especially while she's settling into your home. Try to keep the visitors to the room where she's caged down for a while, it'll do a lot of good.
Also watch your mouth around a Grey.
Anything you say can and will be held against you. Really. A coworker of mine has a Grey who'll hear something once and repeat it---no need to say it twice.
As for food...I prefer pellets. I have three budgies (Pippin, Snow, and Felix), a Peach-Faced Lovebird (I call him L.B., but that's simply for lack of an actual name), and a Green-Cheeked Conure (Jesse James). The Conure will be 4 months old on the 26th of this month, so he's on a whatever-he-will-eat-to-get-his-weight-up diet...mostly seed, fruits, and veggies (supplemented with handfeeding formula, usually offered in a straw or on my finger). He's offered pellets, which he'll eat...when he feels like it. There's really no push with him, but the goal is to get him mostly eating pellets (I'm using Zupreem natural-colored pellets for Cockatiels, and his seed is Ecotrition for Cockatiels, mixed with what I feed the budgies). I've just heard too many horror stories of fatty liver problems and obesity caused by seeds to go completely seed...but I do adjust their diet as needed. The Lovebird is on the same diet as the Conure, and the budgies are on Zupreem rainbow-colored pellets and Ecotrition Parakeet seed. I have them primarily weaned onto the pellets, which has them looking great---very shiny, active, healthy birds. The seeds are mostly a supplement, and constitute less than 25% of the diet. The rest is pellets and fruits and veggies. All 5 of the birds are allowed free access to cuttlebones to keep the beaks trimmed and give them calcium.
Also, all my birds do have clipped wings. It's a personal choice, as I'd rather never lose them. My birds are out of their cages more often than they're in them when I'm home, and I do take them outside with me (always supervised, never out of arms' reach, of course). I keep their wings short enough that they get no vertical lift, but long enough that they fall gently to the ground instead of sinking like a stone.