You are correct, your OS will only boot up faster with a solid-state drive. That being said, if you perform any operating system related task that needs to retrieve data from the drive, it will be much faster then if your OS was on the HDD.
The whole point of a solid-state drive is to decrease application loading times, and that's it for most users. This is more due to the lower seek time rather then the faster transfer rate, which makes it more like RAM (good sustained and random transfer rates). In fact, some users would be better off getting more RAM then a solid-state drive - but that always depends on your needs as the user.
That being said, the main storage device (SSD or HDD) is always the bottleneck of any computer system. While SSDs help to alleviate this bottleneck, new ones are still only ~1/40th the speed of RAM. For example, some memory bandwidth in newer computers has reached over 20,000 MB/s versus some new SSDs which top out at just over 500 MB/s.
You can also use it for the increased sustained transfer speed, but that only applies if you deal with very large file transfers with, for example, video encoding.
For the fastest experience with your computer, install your OS on the solid-state drive, but do remember to make frequent backups. Yes, it will mostly affect just your load times, but again, that's why you put data on a solid-state drive in the first place. They are not meant for storage of large amounts of data, just your OS/programs/games only.
Finally, since most SSDs have a smaller capacity then hard drives, you may wish to "lighten" your OS install by not installing as many packages (if you use a package-based Linux distro), or using a utility to remove components from the installation media (if you use Windows).