2 things, first to correct the above statement: You don't engrave a new serial number, you have to engrave the full name and location [on the receiver] of the entity making the SBR. No abbreviations allowed except those recognized by the post office. This can become a problem depending on how long your name is and where you live:
Millhouse Farnsworth III
Shamballah-Ashrama, CO
For example. This is why trusts with short names are good (though it doesn't help with where you live):
MF TRUST
CO SPRINGS, CO
or
CO SPGS, CO
Note the use of post-office recognized abbreviations. They're the only abbreviations allowed by the ATF. Many people get away with "COLO SPGS" for example, but they're just lucky.
Now for a suggestion. If you're going to make an SBR, especially for your first one, consider a platform that's flexible -- one that you can change calibers, etc. on. Of course, the AR15 is one obvious platform, but another is a Thompson Center G2 Contender or Encore (Or the older, plain Contender) rifles. One huge advantage of the Contender/Encore platform is that if you decide to spend money on a silencer in the future, they're stupid quiet because there's no action cycling. Plus in the rifle configuration, you can buy one at your age.
There, my free advice!
O2