You should simply try a few different ones to see what suits you. Most have free or trial versions. With that said, here's what I use:
PowerAmp (free 15 day trial version available with all features) - I tend to use this one the most. It has a good and pretty logical interface. It's feature set is also good, including the ability to edit id3 tags and download album art, plus nice integration with musiXmatch for lyrics, and projectM for getting psychedelic, man. There are a fair number of sound adjustments, enough to make things sound about right. It has 5 widgets available, 1 for the lock screen. I think I just like the overall look of this one the most, and the sound output is quite pleasing to my amateur ears.
JetAudio Plus (free version available with some minor enhancements locked out, but with ads) - I use this next most often. The interface is good, and though I might like PowerAmp a little more, this interface seems to be more customizable and logical. It has a fair number of features, but lacks id3 editing or lyrics importing (but it can show embedded lyrics). There are, however, many customizations in the settings if you're into the tweak thing. It has the most sound adjustments available, including a 20 band EQ, so getting the right output shouldn't be a problem (or maybe all the adjustments just makes it more difficult!). If widgets are your thing, this one has more varieties (13) than you'll ever need, including 12 available as lock screen widgets.
N7player (14 day trial version available with all features) - No, not n7 as in Nexus 7, but I'm not sure what it stands for. This player has the most original interface of the three listed here, though to me, it's the least intuitive. I use it just for variety from time to time. It has id3 tag editing and album art downloading, plus musiXmatch integration, but seems to maybe have fewer customizations available. It certainly has the least amount of sound adjustments compared to the others, so if that's important to you, then look elsewhere. Also, if you like lots of widget variety, this unfortunately only has 2, and none for the lock screen (other than if a song is playing).
None of the above can stream music, from neither the cloud nor a LAN. They're intended for local playback only.
Of course, I also use Google Music and Amazon MP3 for cloud listening. And occasionally I'll use musiXmatch if I'm reading lyrics (assuming I'm not using the PowerAmp integration). But for full featured players, try the ones mentioned above, or some of the many others listed in the Play Store. Good luck with your choice.