Painting Oak? This is worth a look.
I just ran across a product (I am a member here, not a salesman) that seems like it would do a great job at grain filling, which was my concern when I considered painting our oak cabinets. I know there is another product recommended, however that one I've heard is very tough to sand (hard). This product looks easy to apply, easy to sand. It comes in colors, or in a neutral tint base that will take ANY stain (water or oil base) or paint color and any finish topcoat.
It's called Timermate. I'm going to get some tomorrow for a woodworking project (we're making a mantle shelf). Anyway, just something you may want to investigate, it looks promising.
There are three videos about it here on the left, the one in the middle shows an example of coloring Timbermate and using it for grain filling: