Lead screw whip happens. There are even critical speed charts on them if you feel inclined to search for them.
If you still get whip after you've made sure everything is buttoned up then finish the build first before it worrys you too much. If you get whip after the build is complete then just slow your max velocity down a tad until you're comfortable.
You don't have to be a mechanical or electrical engineer to build a cnc anything. You don't even have to be a machinist, modeler, designer, cnc programmer, or operator. You just do it and rely on learning what you need to as you go from those on the net who came before you. At some point soon, and before you know it, you'll be answering more questions than you're asking....paving the way for those after you and contributing back to the cnc communities that helped get you going.
Congrats on your build. Good luck with the noise. Keep us posted if you find a sufficient silent vac system as there are others with the same needs. You may want to go with a watercooled spindle. They very quiet. They cost though.
Joe

 

I youtubed shop vac silencer cabinent. Whoa there's a lot of great ideas.