My concern is managing the storage
Then something like Back-to-My-Mac is idea. You enable it via System Preferences -> iCloud -> Back to My Mac
Set up and use Back to My Mac - Apple Support
OS X Mavericks: Use Back to My Mac
https://www.apple.com/support/icloud/back-to-my-mac/
It would be nice to be able to upload some MBs every now and then
Not a problem. With Back-to-My-Mac you will be mounting your home Mac's disk read/write, so you can both access as well as store (or update) files on the home Mac from your remote location.
As far as the bandwidth limits, do I need a high upload bandwidth at home?
Not really. If you have at least 1megabit/second uplink speeds, it should be OK, assuming your PDF files are not huge. And may ISPs provide better than 1megabit/sec. If you were going to be doing tons of data access read lots of large files, then the uplink speeds would be more important.
You can always just try it, and if it seems to satisfy your needs, but seems a little slow, you can contact your ISP about increasing your uplinks speeds (which I'm sure they will be happy to do "for a price" 😁 ).
Another concern is opening a hole in my router Firewall to access part of my iMac datas through the Internet.
Back-to-My-Mac on your Home Mac deals with crossing the router. It basically uses a hand-off via an Apple server, so both your home and remote Mac's contact the Apple server which provides contact information, then your home and remote Macs negotiate a direct connection and do authorization (Apple is not involved in the authorization, just your 2 Macs).
The connection that is established is encrypted between your 2 Macs (again, Apple is not involved).
It would be wise to give your home account a strong password, but other than that you do not need to worry about security.