Early 2014 I upgraded my phone to a Sony Xperia Z1. So far I'm quite happy with it.
On their phones Sony provide a music player helpfully called "Music".
The Xperia Z1 comes with Sony's Walkman application installed as its music player.
Shuffle mode on Sony Music player
Initially I couldn't find how to play my music in shuffle mode, so tried a couple of other players.
Google play music did a reasonable job, including a store, but it didn't seem obvious that I could download the tracks I have purchased to store on my PC with the rest of my collection (I have since set its save location to the SD card and tracks can be lifted from there). That put me off.
After trying a couple of other players I ended up trying again to find the Walkman shuffle mode. The first screen I had assumed was just about buying tracks/playing streaming music. I think that's where the confusion came from.
The current (Oct 2014) way I use "shuffe all" is to go to the menu (tap the walkman icon, top left), select library, swipe left/right 'til you get to the 'songs' list.
The Shuffle option's at the top of that page:
Organising music on Sony Xperia
I cheat.
I don't actually do my music organising on the xperia device but on my PC and sync the playlist files across to the phone.
As of yet (Oct 2015) I've not found a way to play all music in a particular genre, indeed that has been confirmed by the Sony Twitter account.