A lot of people have spoken about how iOS 7 screws up the music sorting in the stock Music app. There is no clear solution even in iOS 7.1 (and in fact, it screws up even more if you pick the music through the Artist tab). I'll not beat around the bush: pick an alternative app that will let you sort your music better.
For those that would still like to stick to the stock iOS 7.x music app, there are some workarounds to picking music from an album/artist faster. But then, the inadequacies of the music app is kind of overwhelming that even the workarounds seem a bit stretched.
The Sort Problem
Unlike iOS6, iOS7 sorts music in reverse chronology in the Artists → Album view. For a handful of users, this is okay. For a lot of audiophiles though, this is absolutely not okay. And it's obvious. The most recent music takes a lot of time to become one of our favorites that we listen to. Most of the music that we listen to from an artist's album is from the years bygone. A reverse chronological sorting means you have to spend more time scrolling down to pick the music you want to listen to.
( Note that we're only talking about artists → albums. For a generic sort of albums only, you can go to Music → More → tap on Albums (or drag it to the menu bar) )
The fact that you can't control the sort order of Artists → Albums is simply ridiculous but Apple has been quite the adamant type when it comes to the giving users the sort-control for the iPhone app.
Playlist as a solution
One area where you can still control the sort (through iTunes sync) is the playlist.
On iTunes (PC/Mac), create a new playlist and have all the songs of a particular artist copied/linked to this new playlist. You can sort the playlist as you want within iTunes.
Next up, sync the playlist to your iPhone and the sort order should be carried over.
Obviously, this sort of a thing works optimally for music lovers who have only a handful of artist favorites that you listen to frequently. If your favorite artists run into tens with correspondingly large number of albums/songs, then that's going to be a problem you can solve only using multiple playlists.
Use the search feature
Obviously, the search is only when you're pretty sure of what track/album you want to listen to. I'll admit that even hardcore audiophiles are driven by discovery, not by a sharp idea of “this-is-what-I-want-to-listen-now.” We pick music by scrolling through a list of options we have. But for the moments that you want to pick a particular track or album you have in mind, don't waste time going into the artists menu and then scrolling forever. Use the search bar from the top.
Go for alternatives
Most recently, I stumbled on Picky (suggested by redditors, it's $1.99 on App Store) and this app seems to be specifically designed to address the issue of sorting and arranging your music library. There are many other iPhone music app alternatives too.
Visit this for more iOS 7 related how-tos.