My first thought is: youre going to build a simple web service. Why not avoid doing many things double and go for a great ready-made implementation of a webserver with REST framework, see for example:http://restx.io/
This web service would then offer a back end (retrieving levels, adding levels to the level repository) that would be both useable by a website (if you like) and from within the game itself, be it android or desktop.
For example a HTTP GET from:
<myserver>/levels/newest returns the 100 newest level ids (and name, creator etc)
<myserver>/levels/best returns the 100 best level ids etc
<myserver>/levels/56634 returns a specific level
HTTP POST to:
<myserver> would allow adding new levels (youd need checks for security and to avoid spam though)
I dont think FTP will be particularly suitable for this sort of thing, but I'm not too sure. If you know some web service development this would get you going and conform to many best practices quickly. Otherwise it may be a bit of learning to understand how web services and RESTful services work. Good luck!