I can understand you feeling "forced" to upgrade in the sense that Apple no longer supports what it considers to be obsolete machines and it is not easy to do upgrades now. If you look at support history you generally get about 4 years of support in terms of updates and then you're on your own or relying upon third party sources.
However, you can still find used hardware and software outside of Apple. If you need Tiger you'll have to look to sources such as e-bay, Craigslist, etc. The PowerMac hardware forum, and the specific OS forums are good places to get suggestions if you have a specific question you would like to ask. Although Apple may no longer think it important to keep your old Mac running, there are many of us who have them and do!
You will find you can only go so far, however, and ultimately you'll encounter things (the web especially) that an old machine cannot handle. I find that rather than rushing out with my wallet every two years or so when Apple brings out a new operating system version that I can go for about 10 years. I then upgrade to something that is maybe only 2-6 years old (I never buy new) and in the next 10 years I perhaps do a few minor upgrades (e.g., RAM, bigger hard drive, maybe jump up an OS version or two). I figure over the past 20 years or so I've been going about $100/year average for computer expenses vs. the $1000/year I'd be spending if I was staying on top of things. Of course you can now also see why there's no marketing interest in keeping me in updates.
You can find upgrades on eBay & such, & upgrades Sisk & RAM wise if needed.
To use Mac OS X 10.4 Tiger, your Macintosh needs:
* A PowerPC G3, G4, or G5 processor
* Built-in FireWire
* At least 256 MB of RAM (I recommend 1GB minimum)
* DVD drive (DVD-ROM), Combo (CD-RW/DVD-ROM) or SuperDrive (DVD-R) for installation
* At least 3 GB of free disk space; 4 GB if you install the XCode 2 Developer Tools (I recommend 20GB minimum)
See Tom's, (Texas Mac Man), great info on where/how to find/get Tiger...
Or Ali Brown's great info on where/how to find/get Tiger...
* Mac computer with an Intel, PowerPC G5, or PowerPC G4 (867MHz or faster) processor
minimum system requirements
* 512MB of memory (I say 1.5GB for PPC at least, 2-3GB minimum for IntelMacs)
* DVD drive for installation
* 9GB of available disk space (I say 30GB at least)
There are workarounds if the 867MHz is the only hangup...
So we know more about it...
At the Apple Icon at top left>About this Mac, then click on More Info, then click on Hardware> and report this upto but not including the Serial#...
Model Name: eMac
Model Identifier: PowerMac6,4
Processor Name: PowerPC G4 (1.2)
Processor Speed: 1.42 GHz
Number Of CPUs: 1
L2 Cache (per CPU): 512 KB
Memory: 2 GB
Bus Speed: 167 MHz
Boot ROM Version: 4.9.2f1
I should point out that the processor and RAM requirements for Tiger and Leopard are relatively obsolete by now, you should take them with a grain of salt so to speak. They are about as good as the 233MHz requirement for Windows XP, hah! try running on that today.
The system requirements were fine when the OSes came out but I couldn't imagine running my 10.5 iMac on less than 2GB or my 10.4 PowerBook on less than 1GB. The internet has changed quite a bit in just the past few years, and Adobe Flash which is used for much internet content increases the load on the hardware.
And if you upgrade to 10.5 or later you will have to forgo Classic on that partition, but booting into Mac OS 9 may still be possible:
This tip explains pitfalls for Leopard: https://discussions.apple.com/docs/DOC-2275
This tip for Tiger: https://discussions.apple.com/docs/DOC-2541