If you're looking for a setup that purely sounds good and you don't care about sound leaking get open, closed headphones are just never going to sound better because of physical limitations on the design.
osvaldoOh I see you, but DAC & Amps aren't really meant to change the signature that much, aren't them ? From my understanding, they might color the sound a bit if anything but correct me if I'm wrong here.
depends a lot on the gear in specific - generally speaking a pair of hd800s or something are always going to sound like a pair of hd800s but things are going to sound different depending on what they're hooked up to - whether that's "significant" depends on who you ask and what the comparison is really between. Some headphones are more revealing of what's further up the chain than others - hd650s are an example of this which is part of why that headphone is so popular - it scales with the gear it's hooked up to a lot more than other headphones tend to. Somebody earlier said that you shouldn't spend more on an amp than headphones which is sort of misleading/not always true for cases like this (there are people who use 650s with schiit ragnarok for example).
If you were looking to be cheap I would just get a pair of akg k240s and call it a day, if you're looking to get into actual hifi I would look around at what you can get used since you're going to get a lot more for your money generally - I got a $1000 msrp pair of headphones for 450 used. Otherwise I would say get a schiit modi 2 uber (don't bother with the multibit), hd650s and as big of a class a amp as you can find for them that you're willing to spend on. The schiit fulla and most cheap amps aren't enough for those headphones to really do what they're capable of. I would try looking for a used gustard h10 or maybe schiit asgard.