I've had several dogs of my own and a number of fosters over the years, and I think the best advice I have for you would be to give her a schedule right away. Dogs do great with routine, and starting off with a solid routine in terms of feeding times, crate times, walks, etc. will help make the transition so much easier because she'll know what "comes next" quickly and become comfortable with the routine.
Do make sure to ask what the rescue is feeding and slowly transition from that to a different food (if you plan to do so), rather than just switching her from one day onto the next. I've had a number of fosters that had very sensitive tummies and giving them the runs isn't really the first thing you'd want to do.
When I pick up a dog for transport or to foster, I like to ask that they not be fed that morning, just in case they don't do well with car rides or will get sick. It's not fun starting off a ride to their new home having them barf all over themselves in the crate inside the vehicle. (Or poop, for that matter - walk before loading up for the ride home.)
When I bring one home, I usually unload outside and walk them around the house or in the yard for about ten or twenty minutes before going inside to give a chance to go potty and smell the neighborhood. At that point, I usually don't correct for pulling or anything, I just let them sniff and look.
Once inside the house, I keep the leash on and walk them to where I keep the food/water as well as the crates, and then keep them in the same room with me as I go through my normal routine. This helps me keep an eye on the dog and the dog getting used to the new place. I don't like to let them loose to explore right away, partly because I've always had cats when I did foster.
I usually started crating the first night after bringing a new dog home, whether they've previously been crate trained or not. As you're getting yours from a rescue, she may well be crate trained - do ask about it. Also ask what type of crate they are using. Some dogs are not comfortable in a wire crate and prefer the enclosed plastic airline crates instead. Some can't be trusted with any kind of bedding inside the crate. (I usually have nothing in the crate for a new dog at first.)
Training her will be essentially the same as training a puppy - it's a common misconception that you can't teach an old dog new tricks or that they are "set in their ways". As your new dog will be coming into a new house with new rules and all that, just start her off as if you were starting off a new pup - get her used to her new name (if you will be changing it), work on basics such as come and sit and go from there. I don't usually introduce a clicker for training right away with a new dog, I wait a few days for the dog to get settled in before I start to "really" train.
As far as exercise goes - your dog doesn't get any more exercise dragging you down the road by the lead than she would with you walking briskly next to her ... unless she's jogging down the road while dragging you.
I like using a long line with a new dog ... you can buy them or make your own from rope. I've bought some nice "climbing" rope that was rated to 2,500 pounds strength for about $5 for 50ft. That's really all you need. And a clip to attach it to the collar or harness (I kinda like using a harness with a long line). That way, you can let her "run" in a large, unfenced area (like a local park or soccer field) while maintaining a physical connection.
Another option would be to find an area that is securely fenced. If you don't have a fenced yard, that can be difficult. I've had some good luck with tennis courts in parks as nobody seems to use those anyway and the fences are tall enough to prevent climbing or jumping them.
The other thing about exercise is that physical exercise is good (and needed), but don't underestimate mental exercise in form of training and brain-games. It's more work for a dog to have to sniff out a toy or treat in your house than it is to just aimlessly run around the yard. Make sure to work her dog brain, not just her muscles.
As far as collars go, my general goal is to eventually use only a flat collar. But when you're starting off a new dog and you don't quite know how much she will pull or whether she will back out of a collar, a martingale is usually a good first "go to" collar when bringing them home.
I like the Lupine martingales, the all-fabric kind --> Sunburst Combo Collar | Lupine
as they can act as both a flat collar AND a martingale, so they're a good all-round collar. Plus you can't beat their guarantee.
If you need help controlling her pulling while you work on training, my top two choices for training devices are the front-clip harness and the prong collar. I would use either of those any day before I would ever use a head halter, choke, e-collar, etc.
Most GSDs are very intelligent and, more importantly, WANT to please. They are a breed that wants to be with their handler and wants to work for their handler ... which is a good thing.