@alexis1,
You can use a fairly thin coat of white emulsion on wood to seal that, maybe not pro, but cheap and very effective, normally there's some lying around.
It probably is not absolutely required to prime them, how much 'evenness' you get from priming of any kind will likely be negligible, given the other paint can be purchased to go straight on it, that may be thicker, check the tin for 'primer required' or such.