Once I have removed the linseed oil, can I put some kind of different finish over it?

I have some benches that were treated with a linseed oil/mineral spirits mixture (50/50), and they continue to be sticky. I am going to remove the oil with turpentine and some sanding, and then I would like to either use paint or a solid color stain over the top. What would work best? Is a primer or other sealer necessary? These are permanent outdoor benches, subject to all the elements...