I have one of the older, no-longer-made Kindles, and I've been a fan for quite some time. My thoughts:
If you JUST want to read books, I'm with the majority here: You should go with the plain Kindle. The screen is easy on the eyes (which matters to me since I read for hours at a time), and it works fine in bright sunlight. The screen is superior to anything else on the market right now.
I'll add another reason: Weight. I have an ipad as well, but I much prefer to read with the Kindle because I'm a lay-on-my-back-reader (again, holding it up for some time the weight will matter). I have no idea whether the Kindle Fire is more like my old Kindle or more like the ipad, but it stands to reason that it'd be heavier than the basic version.
However, if I were buying something new, I don't think I'd go with the basic-basic version. I'd go middle-of-the-road. I'd definitely go with the 3G service because it'd be easier to buy books.
I agree with your assessement: I have an ipod for music. I have an ipad for various computing needs. I don't need to spend more, more, more on a one-stop electronic gadget. A basic Kindle does what I want.
As for free books, check Amazon.com about twice a week. You'll find loads of free books -- some that'll interest you, some that won't. When you see something you think you want, grab it. Things
often show up for free, then turn into "for sale items" only hours later. Do not buy a Kindle thinking you'll save money; I'm spending more on books than I did in the past, but I'm also reading more.
Amazon Prime is
not at all important to have with a Kindle. For $80/year it gives you one "rental" per month, and you can only have one "rental" out at a time. Not a great deal -- unless, like my sister-in-law, you're getting Amazon Prime
for free by doing an automatic order every month (she has diapers sent to her automatically each month; not all of us have any need for something "automatic") or unless you order frequently and want it for the free shipping. Unless you have special circumstances, it's better just to pay for the books you want.
On the other hand, if you have any idea that you want your new toy
to do more than just read books, I think the Fire is a good product for a good price. You can't beat it for versitility. I know a handful of people who bought them for Christmas, and they're all pleased. I almost got these for my kids for Christmas, and I still may do it next year. For them, I would go with the Fire because -- unlike me -- they'd do more than just read with it.
In conclusion, you really can't go wrong with either product. You just need to consider exactly what you want to be able to do with it.