How exciting
1: If the crate is for travelling: ask breeder about the parents size since it should not be too big or too small. If you intend to use a crate at home for longer periods of time I would say get the largest size you can fit in your house. Or better yet, get a baby gates to limit access to certain parts of the house so you don't need a crate. Better for the puppy to not be confined to a crate
2: Leash: I think everyone has their own preference. I like having small clips and I like nylon leashes with a clip in each end and several rings for attachement. But that's just my personal preference. I would make sure it is longer than 150cm as a minimum. I like 180cm for loose lead walking in the city and flexi for walking in nature (unless I can have the dog off lead).
3: Yes harness. At least until the dog knows how to walk without pulling. I prefer harness for all dogs as it is safer, but definitely for a happy puppy bouncing around, pulling the leash. An adjustable H-harness should do the trick in the beginning. There are tons of different types and everyone has their favourite. But a simple H harness is always a good start. I've tried several types but went back to this type in the end and have stuck with it for years now. Again preference, but it should fit well and not restrict movement of shoulders or be to high in the neck and that is easy to achieve with an adjustable H-harness.
4: Carrots are safe and can be served cooled. Pressed oxhide is a favorite here. But probably safest to stick with the ground up type that is pressed together. Kong or other toys that can be stuffed (not necessarily just for teething, but a frozen stuffed kong wil keep a pup occupied for a while). I like giving dried meat as well.
5: Treats and books on training and a camera with a huge memory card
Just because you can never get enough pics of the worlds most wonderful dog...your own. Oh and a cheap dogbed as the first one is likely to get nibbled on, if not completely shredded. Best to save the money and upgrade when the puppy stops chewing everything in sight