You should comfortably be able to upgrade to Snow Leopard 10.6.8. To learn more about other peopl's experiences Google iMac 8.1 There are several entries there which suggest it has some difficulties with later OS's. For some reason this model had quite a short sales life, about 11 months.
I could If Apple would let me upgrade the OS from 10.5 to 10.6 but they apparently discontinued all software they were selling so that they let 10.5 users stuck.
Any ideas on how to do the first upgrade?
I wish I could be more positive. I agree that Apple have been rather naughty of late but I keep seeing posts that suggest Snow leopard can be found. In which case it would be easy as the update to 10.6.8 is a combo update.
Suggestions include ... Apple retail stores, Apple premium re-sellers, Amazon and Ebay. The last two being possibly more expensive. Where are you located?
It is a fact of life that Apple only provide update service back two generations and indeed, it appears that with Mountain Lion they have made Lion redundant. The only exceptions are likely to be serious security problems so even with Snow Leopard (the best OS they've had in my opinion) you'll be unsupported.
Best advice I can offer at the moment but hopefully you don't live out in the wilds and without access to Apple stores.
Thank you for the star,
i called apple support asking the same question, they said SURE! we can help you with that. He told me that they could send me a copy of snow leopard for 29.99 and it was that simple. insert the DVD and youre off! Make sure you have enough RAM first tho, i upgraded to 4 gb with the kit from apple, little did i know that there was a tested 6GB kit out there for 20 dollars more but not from apple. OWC sells the 6gb tested RAM kit for 129.99. but yeah, call apple, tell them you want snow leopard, give them your CC number and youre good.