I use Google Music. I believe they allow you to upload up to 20,000 songs for free... way more than I have currently. You need to download and install their Google music manager software... point it at your music folder and let it go.
It could take a few days or more to upload (based on your internet speed.) In my experience it will even upload iTunes music purchase (just not DRM'd ones.... newer albums don't have DRM... purchases from years ago MAY... you'd need to burn those albums to CD in iTunes, and re-rip them before Google would upload it.)
[People complain about how long it takes to upload from PC... but seriously... set it up let it do its thing and in a few days its done; you could easily waste more time looking for another solution.]
Once the music is in the cloud... you can use the Play Music app to stream to your device, or "pin" it (download) for offline listening. It's great having access to all my music any time I want... I used to use other multiple solutions including FTP and stream directly from my home PC... but this is way better.
As far as install of apps; from the Play store on the web you can install remotely to any of your devices. As far as managing apps (like removal) I typically do that on device itself... AirDroid will let you wirelessly transfer data to/from your device... and I think you might even be able to uninstall apps from the PC interface for that. (I've used a few apps to "batch" uninstall apps... but they were clunky without a rooted device.)