Not having a amp is like running a under preforming cpu with a GTX 1080,
you wont hear the details unless you give the headphones the power it needs.
I have a asus xonar stx soundcard with in built amp paired with a sennhieser HD600,
best way to make the most of your purchase is to split your budget in half and get a amp-dac and headphones.
or by everyone's suggestion there could be a awesome cheap amp-dac and spend the rest on some good headphones,
the reason why i say amp-dac is because a high quality amp needs a high quality DAC instead of the mobo headphone connection,
but to get around this you can get a amp-dac combo in the form of a box or get a sound card with a inbuilt amp.
My friend brought this card: https://www.amazon.com/Blaster-Performance-Headphone-Forming-Microphone/dp/B009ISU33E/ref=sr_1_1?ie=UTF8&qid=1475892532&sr=8-1&keywords=soundblaster+z
He has nothing but positive remarks for it in sound quality and it has a 600Ohm amp bult in to handle any headphone,
with the nearly 1K reviews so does everyone else.
Headphones are a personal pref if the reviews mention a warm feel then they refer to the lower to mid tones,
if you dont know what termanology they refer to in tthe reviews read here: http://www.head-fi.org/a/describing-sound-a-glossary
P.S. Once you have brought your headphone and amp, whatever you end up choosing, look up the term headphone burning in and lossles audio codec.