$800 can get you a very nice frame, Lugged Leader, Wabi, Soma Rush, Toyo Godzilla, BareKnuckle, vintage frames on eBay..etc etc.

Omnium will be compatible with the Pake, Pake IMO are perfect beater builds, slightly on the heavy side but they are perfectly fine. 165mm indicates crank arms length and 144mm is Omnium's BCD.