Macro photography with a Nikon dx body?

Ok so macro photography is something very new to me, but has always seemed very fascinating and fun.

To start off I have a Nikon D5000 so I can't even really consider any AF-D lenses if I want to still have auto-focus. I've been looking into things such as the 85mm f/3.5 DX and the 60mm f/2.8 FX. To be completely honest, I don't know if either of these would do the trick for macro photography or even how good/bad of an idea it would be to use a full frame lense on a dx camera.

Any kind of advice on what I should be looking for with this sort of thing would be awesome as well as knowing possible third party lenses that would do the trick for this like Sigma or Tokina.

If possible, I'd like to stay in the price range of $600 or less.

Thanks anyone and everyone for the help.

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