Sauron was most definitely not an eyeball. I can quote many, many sources for this, but I'll quote the two main ones.
This is a quote from Tolkien's letter #246, where he's talking about Sauron in the
Third Age, not the Second or First.
Quote:
Sauron should be thought of as very terrible. The form that he took was that of a man of more than human stature, but not gigantic.
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Can it get any clearer than that?
Quote:
'Yes, He has only four on the Black Hand, but they are enough,' said Gollum, shuddering.
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There is a rather large chance that Gollum actually saw Sauron during his...visit...to Mordor. Thus, he would know

I can't really see an eyeball as having a hand.
There are other evidences that show that Sauron was not an eye. Tolkien once describes what WOULD have happened if Gollum did not bite off Frodo's finger and fall in Mount Doom. Frodo would try to command the Nazguls with the Ring, and they would obey him, to some extent. Instead of forcing him, they would try to coax him into coming out of Mt. Doom (They would still follow Sauron's orders more than Frodo's though). Here, Tolkien says that eventually Sauron himself would come and wrest the Ring from Frodo. Unless an eyeball comes and tackles Frodo, I don't see how that could happen.
That aside, I didn't really like the movie version of Sauron either. It just didn't have the 'mystical' feeling that it did in the book. In the book, Sauron rarely appears, and none of the fellowship actually see him. He's somewhat shrouded in mystery. In the movie, they take him out, give him a shape, and show him off like some sort of...eyeball