As a former Uzi owner, just a heads up. Uzis were created as submachine guns. They are amongst the best submachine guns ever made and are a blast to shoot in FA. Being in California, we cannot SBR modern guns or have the folding stock so, I was stuck with a wooden stocked, 11lb, semi auto carbine with a 16" barrel and a bullet button. Neutered to the point of uselessness by ridiculous, pointless gun laws. I shot it once and sold it. In a free state, if you can have the folding stock and the 10.5" barrel by SBRing it, they are okay. But even though, it's hard to get excited by a machine gun that has been neutered to only shoot semi-auto. And they are really heavy. Fun for new shooters and those who are recoil averse though but for most of us, meh, not fun to shoot.
Building one could be a fun project but just wanted to give you my impressions having owned one.