Recently (past 1-3 years), Verizon's LTE phones come with GSM legacy support and are unlocked (meaning you can put a AT&T/T-mobile/ANY GSM sim card in, and have it work)
iPhone 5S, S5, S4, Droid DNA, ... a lot of phones work
metroPCS and t-mobile are merging their GSM/LTE networks, and metro's CDMA network is going away. basically, treat metro as though it were a GSM provider (can BYOD, do anything)
you just need to check whether the bands are compatible.
2G- typically all phones are quad-band GSM, and would work
3G- T-mobile(and metroPCS) uses AWS, some phones don't support AWS 3G. also, some phones don't support the DC-HSPA 42mbps network that t-mobile uses (you should still get 3G up to 21mbps)
4G LTE - t-mobile uses bands 2, 4(AWS, 1900PCS) and 12... verizon uses 4 and 17. you should be able to get band 4 LTE at minimum
VoLTE - verizon doesn't have VoLTE support yet (and since they approve all phone updates, no Verizon phones support VoLTE yet)