Here are the specs. What are my options?
CPU Type: PowerPC G4 (1.5)
That's the key line; it means that your sister cannot go any further in OS X than 10.5.8 Leopard, since both Snow Leopard and Lion are Intel only.
Her only option other than upgrading her Mac is purchasing a Leopard
Retail, i.e. universal install disc; they have been going on eBay for in the range of $140/$150 recently. (Be certain to heed joemikeb's caveats.)
Edit: As far as Leopard goes, it's worth noting that
- Apple no longer supports Safari for Leopard, although the final version does support extensions.
- Apple still supports iTunes for Leopard, but there's no way of knowing how long that will continue.