1. Suits: As a direct reply to your question, I would say that from personal experience 3-6 suits are sufficient. Some colleagues tend to take 2 suits with them per week, some take 1 suit per week, and some take 1 suit and have a pair of extra pants for each suit. Depends on your preference, although it's probably good not to wear the same suit for more than a week.
2. Shirts & Shoes: 15-20 shirts should suffice, depending on project dresscode it might not always be blue suit/white shirt, but could be a bit more alternating. Don't forget some good, leather shoes to fit with your suits - focus on black and dark brown shoes.
3. Luggage: In terms of luggage, you should definitely have a good piece of hand luggage, since you will be using it a lot. Focus on a trolley with 4 rolls that is stable and ideally comes with a guarantee. Classical consultant brand: Rimowa. Alternatively, there are brands like Samsonite or less pricey alternatives like "Hauptstadtkoffer" that you can try. The classical case is Rimowa for sure (also as status symbol).
4. Additional To-Dos before starting: What is at least as important as dressing and luggage: get informed about hotel and airline loyalty programs, enroll before you start working and have all the apps (Miles & More, Lufthansa, MyTaxi/ShareNow, DriveNow, Marriott Bonvoy, Radisson, etc.). Enter these loyalty card numbers during your onboarding on your first days of work. You will collect a lot of points and miles, so be ready to collect from day one and don't waste any valuable time during trainings or projects with this administrative stuff.
Have a great and successful start!