Well, the truth is that most of the space used in / is in /user. /var is a work area, and unless you are compiling programs and putting them in /opt, then /opt is going to be empty. Some games may install in /opt, but none that I know of in the repos. My /opt has zero, nada, nothing in it. Ubuntu doesn't use /opt for any of its' default installs, to my knowledge.
If it was me, I wouldn't put but about 4 Gig. in /. No more than 5 Gig. That is over kill just to make sure /tmp doesn't ever overload anything.
I am using the KDE version, which is bigger than Gnome. I have lots of extra programs on mine for testing and play. As an example, I have three different office suites installed. My total install, including /home is only 7.5 Gig. Of course I use data partitions for my data. My /user is 5.3 Gig. That is where all your program files go. As you can see everything else including the /home config files is only a bit over 2 Gig.
In your case, since you want to split it up, I would probably go with 8 - 10 Gig. /user, 2 Gig. /var, 4 - 5 Gig. /, 8 - 10 Gig. /home, and your data partitions. If you think you will have a lot of special programs that you will put in /opt then make an /opt partition of whatever size you think is appropriate. As you can see that gives you lots of expansion room.
The bottom line is, you know your needs better than I do so size according to what you think is best. One thing you can do to conserve resources is to use the ext2 file system on the /user partition. /user is very seldom written to so a journaling file system on /user doesn't buy you much and costs you cpu cycles and drive space. Just remember. The larger your partitions are and the farther they are from the top of the partition table, the slower they will be. Also, there is no law that says you can't expand a partition later if you need more space. You don't have to commit all your space up front. You can always save some unallocated space to use later where ever you need it.