The result is going to depend a lot on the way the wood was sawed.
Apart from that, really anything you put on it is going to make the grain pop. After sanding to around 220, try rubbing some mineral spirits on it and that will show you what just a polyurethane will likely look like. It might surprise you what a "clear" finish can do to enrich the wood grain. Often times with finishing, less is more, as they say.
I will advise - the oak will finish different than the pine. Pine is notoriously blotchy when when stain is applied, and unless you use a grain filler (not wood filler/putty), oak can have issues with deep grain and texture problems later on.
Post a picture if you can of the pieces together and maybe we can better suggest some options? Like I said, try rubbing some MS on it to see if you like the look of a clear finish; then think about colored stains.