yep, you need a serial number for your form. you also can only list 1 caliber (5.56 for instance). no more multi caliber forms are accepted. after the form is approved though, you can have as many uppers and calibers and barrel lengths you want on your SBR. confused yet? just ask away, SBR's are fun and very versatile.
my suggestion, purely my suggestion and nothing else... if building from scratch, buy your parts if or when you can. availability kind of sucks right now. i like building AR stuff and i'm grateful other members here have helped me out a ton. or you can just buy a standard AR and have the barrel cut down after your Form 1 is approved.
ETA:
oh yea, Sean brought up a good point...
3 ways to SBR:
1. Form 4... pre-assembled SBR from dealer (or individual) to you
2. Form 1... cutting down a standard AR barrel or buying a pre-built SBR/pistol upper
3. Form 1... building SBR from scratch.