Before you install Panther, you need to know how much RAM you have.
To find out about your RAM, once again go to the top left corner (where the Apple icon is, right at the top) and click and click on “About this computer.” Right under the information about what OS you are running, it should list actual memory (and it’ll also list virtual memory, which isn’t what you want to know right now). If you’ve got this model of iMac, for instance, you can only go up to a max of 256 megs, and that’s really the minimum for OS X. It’ll run, but pokey. Plus, you’d have to pay to have the RAM upgraded. For the cost of upgrading the RAM (parts and labor, unless you want to crack open the case yourself), you could almost buy a used Blue and White (Code Name: Yosemite :D) G3 tower on eBay, I think.
Frankly, unless you have enough RAM, I think you’d be better off using OS 9.1 or OS 9.2. You’ll run pretty snappy in OS 9.
To find out how much hard drive you have, click (highlight) the “Macintosh HD” icon (or whatever it’s called—it’ll probably be a square disk-like icon) and go to “File >> Get Info” (or better yet, press the Apple key + i). That will tell you how much hard drive you’ve got total, and how much free space you’ve got.
There’s a lot you can get done on a Mac running OS 9. I know there’s an older version of Final Cut Pro available for it, of course versions of Photoshop, plenty of Internet software, Microsoft Office, etc. I’m sure some of us Mac Dopers can help you with obtaining Classic freeware or shareware, or else pass along some Classic software that we don’t use anymore since porting over to OS X.
To further identify your particular model of iMac, check out this page. Also, check out Apple Discussions. They are a very friendly bunch of folks there. I’ve been seeing a big influx of first-time Mac people (coming from all-PC) in the Mac Mini area, and they all comment about how helpful and welcoming everyone is.