Beyer DT770 PRO 80ohm
AudioTechnica WS99 or A900X
Ultrasone HFI 580 or PRO 750
No real need for portable amps, but if you want, the Fiio E11 would be a good way to start on a budget.
If you just listen at home, the Fiio E10 would be a very good way to start on a budget.
If you want both home and portability, look into the Fiio E17.
And used/refurb is always a great way to go on a budget.