Hello Billy, can you let us know the specs of your iMac - any G5 iMac can do what I'm about to suggest but your amount of memory might be critical?
Firstly, I can reassure you all is not a loss, there's plenty your iMac can do and for making music you've hit gold

Garageband is a great piece of software and despite looking and feeling like a user friendly, dumbed down iApp, it is very useful. It has onboard virtual instruments, beats and loops etc but where it really excels is the guitar modeling - plug a guitar in (or any instrument) and you can apply a wealth of effects, processing and amp models etc. The line input on the iMac is great for this - you just might need to get the appropriate cable or adapter.
Logic is the more 'grown up' version of Garageband - you can actually use all the instruments, effects and loops from Garageband too, aswell and all the Logic ones.
Obviously, it's capabilities are far greater too being a more studio orientated package.
Also look up Propellerheads Reason, Renoise and Reaper - there's many others but it all depends on what your requirements are?
A good rule of thumb is to use software that the machine was designed for, from the time is was launched/in use - it's tempting to use the last software version that the machine is capable of running but often the results arent great - better to use software the machine has specs to cover easily.
For web browsing you have Safari and TenFourFox - those two choices spilt users on preference - this is my take.
For any security sensitive browsing, TFF is a must, for everything else I go Safari. You must download Webkit though - this is a 'overhaul' for Safari and is more updated for modern web. For viewing Youtube, I use the ClickToPlugin extension - this replaces any Flash content with an option menu to either, watch flash, watch FLV, watch/download mp4 or open in Quicktime. Doing this, it allows the browser to pass the video file into a more efficient player. It's best to update Quicktime and install Perian with this too.
TFF has Quicktime enabler which has similar but more limited options but I find it refuses to open too many videos.
I've had all the above apart from Garageband (which almost definitely would work but I've haven't installed it) running on G4 iBooks and Powerbooks, so your iMac can easily cope....and it goes without saying, when I last had a G5 iMac, it coped aswell
It will require some research and understanding but there's lots your iMac can do.
I might add, that my Dual G5 serves me for every task, so still in 2015, I don't need to 'switch' yet!
If you need any specific pointers, just ask.