Is this model too outdated to be any use for the next 2 to 3 years? Any guidance would be appreciated.
Is your recipient a power user? From a power user's perspective, the short answer: yes, too outdated.
The cutoff for OSX 10.10 is mid-2007 iMacs or newer. It is likely with the next OSX major update, this machine will be dropped. Also, the specs of that machine are horrible. 2 gig Ram (horrible), slow and small hard drive, and an outdated screen which is blown away by modern displays. No USB 3.0, bad; Firewire is dead, no one is using it, not even Apple anymore. I wouldn't work on this thing if it were given to me for free. And it would absolutely choke on some of the modern work programs, or "applications" in Apple parlance. You can forget about getting anything real work done, if that work involves compiling, database applications, video editing. Heck, even the MS Office suite would be really annoying on this thing.
Having said this, if your younger sibling is going to do nothing more than post on Facebook or play Youtube videos, this will do the job. But so will a brand-new Chromebook, with a superior display, and for only $199.
So my point is, if you are picking up a desktop Apple to get real work done, you need to get something more modern, and raise the budget, else it's going to be a real disappointment. And if instead it's going to be used for entertainment, seems to me there are superior alternatives in your pricerange that will deliver a brand-new device with better specs. Outdated tech is outdated, no matter the logo on the front.