I wish there were a place to audition this equipment. So many people buy one thing, and then they hear that "if you just get an amp, or a better amp, that problem will clear up", or something like that. Then it doesn't clear up, and all that money was spent....
There's a dramatic difference between headphones in price ranges of $250, $350, $450 and so on, on average (some exceptions). But the difference an amp offers is very, very small compared to a difference in headphones. Unless you need the amp to get better volume with an inefficient headphone. I see a lot of posts about getting better bass, or more bass control or damping with a headphone amp. That raises red flags for me, because I have to ask why the 'phone is suffering a bass or damping or other problem in the first place. Impedance mismatch maybe? Or maybe just not a strong enough volume from the player, and the player's sound on the 'phone at max volume doesn't have the same balance as it does at mid volume.
In any case, I really don't think splitting your money to a 'phone and amp is a good idea on a limited budget unless you're sure you need the amp.