Core Music Player is the best local music player in the Windows Store.
You can play and manage the music files in any folders on your phone include SD card directly in the app. Also it supports Music Library that is classic music category feature.

Background playback is supported as well with user-created playlists. All of the interfaces and features are powerful, stable and easy to use if you're familiar with metro UI. You can find a lot of detailed features in the settings and menus.

FEATURES:

Supported playback file types
mp3, mp4, aac, flac, wav, wma, 3gp, 3g2, amr, m4a, mpr
(Supported bitrates of each codecs are depending on your device and OS version)

File and folder management
create, open, delete, rename, copy, move

Folder navigation
favorite folders, expanded sd card folders, go back, go previous, go forward, open containing folder,

Music library
artists, albums, songs, genres, years, new, background sync

Selecting to play
single or multiple files, playlists, history, single or multiple folders, including or excluding entire subfolders

Reordering playlist and NowPlaying
shuffle, sort by name, manual redorder, restore original sequence, overriding player sequence mode, duplicate, remove duplication, find in list

Misc features
search, history, sleep timer, pin playlist to start, pin folder to start, playback control tiles, show state and album art on the live tile, local volume control, fast skip control