As for headphones I have two recommendations for you, at different levels, which are both available on here. They both don't require any additional DAC/amp beyond a phone or tablet/laptop/computer, though you will get more out of them with better gear down the road:
(1) Koss Porta Pro (X) with Yaxi pads - simply one of the most musical headphones I've ever heard, with most impressive subbass impact, midbass punch, very forward and full vocals, and laid back but detailed highs. One of the most non-fatiguing headphones as well. The absolute best bargain in audio at under $50 total and I prefer to listen to it over the HD58X most of the time. The absolute best $50 you will ever spend on audio gear, ~$37 for Porta Pro X and ~$12 for the Yaxi pads
(2) Sennheiser HD58X - absolutely great neutralish headphone with slightly elevated bass that will be a great foundation/starting point benchmark for higher end gear. Does everything well and sounds great doing it, scales well with better gear too. Can't really think of any headphone under $150 that is technically better than it, including the Koss Porta Pros with Yaxi pads.