Allow initially unknown, in-use applications

Using Fortigate 80F v6.4.10.
I'm starting with an edict to "block all outgoing ports".  Obviously, that's not going to work and keep reasonable internet service.  If doing this on a port basis, it seems that one would first set up instrumentation (logging) to see what's going on before an approach for parsing into "block/allow" can be done.  

I should add that I'm trying to use Policy-based NGFW mode and expect to "block/allow" Applications instead of just ports.

I have a syslog server set up and am wondering what to use for search/filter in identifying outgoing application traffic.  What is typically done for this?  I only ask because I've not seen traffic in the log that I might expect.  I guess ports 80 and 443 might be a good starting point perhaps to just identify IP addresses and other pertinent appplication info for building a rule??

I believe that one can come at this rather tangentially with the Fortigate by blocking all but known important "in use" applications - as long as they are in the database.  But, this leaves things that aren't in the database and, particulary those that would be "allowed" - assuming that most "blocked" apps are already listed.  

I'm not sure my thinking is clear on all this.

So, some guidance would be greatly appreciated.  At this stage, I'm more interested in the "what?" and a little less on details of "how?".  All good advice appreciated!