Hi,
What an exciting time for you! Very envious, I love puppies. I'm broody for a second dog.
For the journey home, it depends on the size of puppy and the distance involved but generally I've sat in the back of the car with pup beside me in a box or bed, although some were crated due to distance involved and size of puppy. I wouldn't recommend front seat passenger holding pup as it's a distraction for the driver.
A puppy is likely to cry during the first few nights away from mum and siblings, so I generally spend a few nights on the sofa to be close to them. Some people take the crate up to the bedroom to start with, but it can depend on size of pup and where you ultimately want them to sleep.
Crate training, I can't advise because mine are free range from the start. I gate off the stairs (puppies shouldn't be allowed to run up and down stairs, it's bad for their joints), but my pups have freedom of three rooms during the day and two rooms to sleep in at night.
If you want pup to get used to wandering, you need to puppy proof as much as you can. Making sure there are no cables or wires they can chew on and nothing they can get hold of that might harm them. It's worth investing in an anti-chewing spray for when they start having a nibble on anything they shouldn't.
A play pen can be helpful to restrict them to one area and dog gates/baby gates are vital for giving the family some peace from being nipped.
There is a puppy survival thread and that can save your sanity during the teething phase.
Enjoy your new family member.