Types of giants???

[Secret Fire]

There is only one kind of Giant in Middle-earth: the kind that doesn't exist.

Not necessarily correct, in the Hobbit, Gandalf states, after the company escapes from thre misty mountain goblins that he would have to find a somewhat friendly giant to block up the passage again, so there were giants in the works of JRRT. As far as what they were, JRRT never says.

Bilbo, when riddling with Gollum (the Time-riddle), sits there thinking of all the terrible Ogres, Giants and Dragons. But I think this is simply mythology... and if not, there's no name or deed mentioned in LotR carried out by a Giant.

That's a very innteresting point, but Tolkien believed that every myth and legend is based in fact and so were Gandalf and Aragorn, specifically noted in the Ioreth dialogue.