200mm vs 300mm and teleconverters

[Boden]

Nikon D80.

I'm having a hard time getting close to certain small subjects that unfortunately don't want me getting too close

I currently have a 200mm lens. I'm not sure how this all works. What would a 300mm lens do for me? Would my subject simply be 1.5X larger or is there more to it than that?

Also, someone was explaining teleconverters to me once and I was lost. Something about the sensor size of the camera. Basically it was implied that it's not just a simple multiplication.

Can somebody help me out here with some real simple discussion?

Basically what I'm looking at is an affordable 300mm zoom, which is doable compared to a 400mm zoom which is out of the question. I'm also looking at 1.4X teleconverters. Or a combination of both. Would my 200mm with a 1.4X be roughly equivalent to a 300mm in terms of magnification? I understand the loss of light and potential for autofocus failure - thankfully these subjects are very brightly lit.