Personally, I'd keep the natural timber look and use either a varnish, oil or distress them with a semi-transparent paint. It really comes down to personal preference but one of the unique qualities of pallet wood is the rustic timber look. If you wanted to paint them I would suggest using a water-based enamel such as Dulux Aquanamel.
I'm a big fan of distressing timber like this and you'll find some great techniques you can use in this step-by-step article: D.I.Y. Decorative Vintage Ladder. I've included below a picture of some pallet projects where I have used Dulux chalk effect paint and Rust-oleum chalked then sanded back through them to create a shabby chic look. I also use a homemade distressing tool to age the timber creating wear and tear.
I'd encourage you to have fun with it, try some different techniques and see where you end up. You can always sand it back off if you don't like the result. I look forward to seeing what you come up with.
Please let me know if you need further information or have any questions.