I'm starting out with photography and currently have a D3100 with the 18-55mm kit lens. I want to get an entry level telephoto, but my research has led me to conclude that if I stick with this I'll eventually want to switch to the FX format body, so I'm looking for an FX telephoto lens. Because the DX body of the D3100 does not have a focus motor, I need a lens with integrated autofocus motor. The only lens I saw that fit what I'm looking for had no motor.
I don't much care about the minimum focal length. I'd like the max to be around 300mm. I guess a 200mm FX lens would be almost 300mm on my camera, but not quite the length I'd like if I upgrade.
Are these criteria reasonable? Will I be able to find anything below $200?
Edit: Or are all FX format lenses motorless because they are intended for the larger body cameras with motor in them. Logically this makes sense because if you're carrying multiple lenses that's just useless added weight.