I'm not an ABE expert, just set it up a few times to play (Which is why I wouldn't charge someone).. so there might be other ways people have got it going... but the default, out of the box way is to have the block files on the server as MySQL...If you have bitcoin-qt running then the database can also get updated by its self as it see's new data.
You could have a separate web server and Mysql/Bitcoin server though.. The webserver could/would be accessible to the internet and SQL is connected privately, if required..
I will help you setup and operate ABE for free if you like.
You'll need to organize a server, perhaps a VPS or something to host it on.. and install Linux.
Instead of doing it myself... I can tell you what to do so you learn how to do it and don't need to worry about handing over any passwords or anything.
If one tries to run ABE for Bitcoin, then is it required to run a full node on the same VPS ?