Old preconceptions die hard but the truth is on board audio line outs are generally now very good indeed.
Converter technology is so advanced and the turnover and competition in the motherboard market so fierce it's rare to find a poor line out.
Depending on the impedance and quality of your headphones you might want an amp. FiiO E5 is good and cheap.
Until you have spend over $300 on your 'phones or speakers getting a separate DAC doesn't make financial sense unless you need one or more of the features on offer.
That said. At some point you are going to want to own an audio interface of some kind. I
t's so much more convenient and expands the options available. Try and save up until you can afford something that also offers decent inputs and more than one stereo pair out. Look at the bundled software. You can often get excellent EQ and effects packages as part of the deal.