Capturing a video of a projector image
(1)  You mention 60 Hz for both frame and capture rates so the following should not be an issue, and it's obvious enough, but I mention it "just in case" as such things can trip you up. 

I'd have expected that if your frame capture lasted exactly "one frame" that brightness variation would not be a major issue. If capture time is less than  frame time then location of your capture window affects result. If capture time is > frame time you get a whole image and then part of another. Both arrangements can (will) affect image quality. 

(2) Frame sync signal: 

Camera synchronisation to the VGA signal should be easy. 

The VGA signal set includes a Vsync (Vertical Synchronisation) signal that allows the start of the frame to be detected.

This is on pin 14 on a PC (DB15) video connector and on pin 12 on a Macintosh video connector.  



The above diagram is from Javier Valcarce's Personal Website - VGA Video Signal Format and Timing

To add to the fun the polarity of the sync signal varies with resolution,but that's liable to not worry you once you work out which of he two possibilities applies in your case. 

Assuming that you can synchronise the camera triggering to this signal (seems likely to be simple enough). Worst case you may have to add a fixed delay to move the picture phase into the correct location for you operation.



VGA timing:



Polarity is inverted for some resolutions.

From VGA video signal generation