here is the lowdown:
the akg q701 is 62ohm resistance. typically many boards would handle this though it appears your onboard amplifier on the onboard sound is rather weak so you do need an amp of some sort. this is not all that uncommon with lower end boards.
now, do you go with soundcard or external soundcard or amplifier or soundcard + amplifier or dac + amplifier? a brief overview:
soundcard: will give you the ability to run virtual surround on the headphones if you intend to use them for gaming. whether or not this is important depends on if you use virtual or not. something like the Z has enough power to drive these headphones and is a good choice without breaking the bank
external soundcard: if you are using a laptop which can not use internal cards and still want virtual surround as an option. the creative omni is a good choice here without breaking the bank.
soundcard + amplifier: the onboard amplifier on something like the Z is rather powerful but many times the amps you can buy external can do a much better job of driving headphones and really push them to the limit/give you the most you can out of them. i was reading a forum about the q701 and omni/z and amp and the user stated that the z/omni drove them fine but the external amp sounded a bit better to them. they ended up using the soundcard for processing and sending out the signal to the amp for boosting. this would also give you virtual surround as an option but is one of the somewhat more pricey options though still under budget.
amplifier: if you are happy with the quality of your onboard sound and if it offers the features you want (not sure if it supports virtual, many do not) then just adding an amplifier will boost the volume and make the headphones sound better. however, the quality of the stream will not increase and if your onboard sound has any hiss, pops, buzzing, distortion, etcetera you will hear it. good choice if you want to take things step by step to spend the least possible. an external amp is generally going to be much more powerful than internal ones and much better for headphones. something like the schiit magni is perfect. if you dont want to spend that much, some of the fiio amplifiers are not bad but are not as powerful. keep in mind that unless your onboard supports virtual surround you will not have this.
dac + amplifier: if you wanted to improve sound quality this is a good choice. keep in mind that sound will be stereo only as external dac's do not support virtual surround generally. due to being outside the case electrical noise is very low so offers great quality sound. a great pairup is the shiit magni + modi though fiio does offer some less peforming options like the e17k which may work for your needs.
note: razer does make a free virtual surround software which may work with usb dac's or may not. you may want to look into it if you wanted to go the external dac option. this is processed by your cpu i believe instead of via any soundcard in your pc.
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what is the cheapest option? the creative Z is a good choice.
what gives you the most options? either the creative Z or xonar dx paired with the magni amp.
what has the best sound? modi and magni
other things worth noting on the budget? audioengine d1 amp+dac isnt bad. not as powerful as magni/modi combo but offers a few more options. fiio e10k/e17k are worth looking at if modi/magni combo (which is great for the price) seems a bit too costly.