How far you can update your software is limited by your hardware, i.e. your Mac computer.
Without knowing the details of your iMac you may already be at the limit.
I suggest you download this informative software from this site
and find your machine to explore its software limits.
If you are able to upgrade beyond 10.4 Tiger, newer software will have to be purchased privately from ebay or such and that can be expensive. Basically, Apple's business model is to encourage you to buy a new computer every couple of years.
Some people who prefer not to do this, must be willing to accept some compromise in order to keep running an older machine. Respondents for this '10.3 and earlier forum' would be inclined to this disposition, but a still useable Apple OS is really Mac OS 10.6 Snow Leopard. Earlier stuff will work to varying degrees but only with some struggle.