What type of paint to repair my wooden veneer?
Matching paints and colours can be a science in itself. No matter what you do the chances of it match perfectly are close to none. I don't have much advice to offer when it comes to painting. But...

Not an answer to your exact question but wanted to offer a different suggestion then painting. Why not just patch the veneer? One the first obvious questions would be I can't find something that matches. You don't really need to anyway.

There are plenty of people who patch veneers are both old an modern furniture whether the end result is meant to be a simple repair or to add an accent.

It does not have to be a simple square patch either. You have the opportunity to make something truly special and unique. In it simplest form find some existing veneers, thin scrap wood etc. 

Severally simplified steps 

I don't image you are going to do this anyways.


Cut a shape you would like that compliments the damaged area. It is actually preferred that it be slightly thicker than what you are replacing. 
Remove any extra remaining veneer are the area. Use the patch you created in the previous step as a template. 
Clean the "void" and fill in if damage is severe. (You could use plastic glue in your case)
Glue in place. 
Sand down. Card scrapers are useful here but not something everyone has. Careful around the existing veneer.
Finish as desired.


There are many tutorial examples out there but here is one where a table with a cigarette burn was patched and finished. 


Mid Century Table Veneer Repair