I have tried over and over again to paint first, then veneer - hoping to avoid having to mask off the veneer. This DOES NOT WORK. No matter how careful you are, some veneer glue will get on your paint, and even if it doesn't your flush trim bit will damage the paint. Beyond that you still have to sand the corners of the veneer slightly which will also damage the paint. Trust me - veneer first. I have found however that masking off the veneer is not bad at all - I decided to try using contact paper (stuff used for drawer liners) and it works fantastically well. Get the stuff that says the adhesive is removable. They come in rolls about 20" wide by 15' long for 5 or 6 bucks a roll. It covers everything and comes off easily. I use a razor blade to trim the edges right up to the edge - creates a perfect paint to veneer line. Then pull off the contact paper, sand, and finish the veneer. Do not sand the veneer before the contact paper goes on other than to gently take the sharp corners off.