Good starter lens for macro images?

I have a nikon D3100 and I love to take picture of plants, the lens I currently use doesn't get good close ups and I'd like to see if there are any (relatively) cheap starter level lenses for me.

The Nikkor AF-S 40 mm macro f/2.8 would be the best and actually the least expensive, under $280.

One of the more popular macro lenses is the Nikkor AF-S 105 mm macro f/2.8 because it allows the shooter to be further a way from the subjects. It costs about $985. As you can see, the 40 mm is a less expensive starter level macro lens.

NOTE: While the 40 mm is inexpensive, it is NOT cheap. The word "cheap" insinuates that the lens is poorly made and of poor quality

Tamron 90/2,8 or any 50mm prime lens with extension tubes

First, get the most out of your current kit lens. Put it in the close-up mode and see if that is what you want. After that, you need macro (or micro) lenses.

The lens your camera came with, 18-55 VR actually let you get pretty close. I'd start with that.

Once, I took an image of a bee feasting on a flower using my D60, which is two generations older than your model. I was using 18-55. When I cropped it close, I could clearly see the bee was carrying two pollen balls on his legs. I could even see individual particles of pollen on the ball. I was able to print it on 8.5x11 paper with some noticeable pixels but not badly. That's not bad for a cheap kit lens.

Otherwise, you could go with Nikon's 40mm or Tamron's 60mm. They are both highly rated.
I personally have a 105mm VR but that's probably too much for your needs.