Nikon 70-200 f/2.8 VR 1 vs. f/4G

Pardon my low level of knowledge in the following. I have a D90 with the Nikkor 18-105 f/3.5-5.6 kit lens.  I've had the setup for several years and know I want a faster, longer lens for lower light situations such as indoor no flash, sports in artificial light, etc.  My skills and use generally are limited to setting f/stop and/or shutter speed based on the situation, otherwise making pretty minor adjustments to the camera default settings.   The Nikon 70-200 f/2.8 VR II is overkill for me and I don't want to pay that much, so I'm looking at maybe a used Nikon 70-200 f/2.8 VR I, but there's also the new 70-200 f/4G VR.  Part of my ignorance is that I don't know how to compare the speed of the f/4G to what I have now, i.e., f/3.5-5.6:  will the f/4G in generally be a big improvement in speed in my shooting uses?  Am I better off getting the f/4G in order to have the newest VR and other tech, or getting a used f/2.8 VR I?

Also, I've seen suggestions the f/4G is optimized for FX, and I have DX format, or am I misreading and it's merely that the f/4G is suitable for FX as well as DX?

I also feel pretty sure I'd rather have one of the Nikon options rather than a new version of a 70-200 f/2.8 with image stabilization by some other maker like Sigma.  Given my price range as indicated above, is there some non-Nikon lens that's clearly a better choice for what I want?

Thanks for any feedback.