You want to use stain, dye or just finish?

The two woods will not look the same color shade even with the same colorant.

Trim should be stained/finished before installing.

To get the same tones, the same species wood has to be used---unless you do a LOT of experimentation to get close with different recipes of colorant.

I have a personal dislike for painting oak---the grain shows and instead of smooth surfaces, it looks like painted oak---which it terrible, IMHO.

And pine blotches quite a bit without prestain treatments. Which are usually made by the applier---1# cuts of shellac for instance. And stains for pine are usually recipes of three or more different stains to get the pine to look decent.

You might just stain the oak---that is fairly simple and paint the doors.

If you were experienced in finishing I would agree with Handy. Since you say you are not a pro,I differ in a couple of areas. Combining colors is an art best left to the pros who have lots of pratice and hone their skill with each new project. Min-wax is not popular with pros but imo is user friendly and reasonably durable. I suggest you look at their color chart for a color you like. I think when you see the examples of your color on oak and pine,it will please you. Shellac is a wonderful product if the user knows what perportion of alcohol to use for the desired result but sticking to Min-wax products including their pre-stain yields fairly predictable results. I am refering to thier oil base system. For goodness sake do not use Poly-shades. It's a mess and impossiable to get good results with. Although the pre-stain is the easiest part of the project, many people fail to do it properly because they wait too long to apply stain. Depending on your speed, do only as many doors/sides that alows honoring time between pre-stain and stain. Oak does not need pre-stain. The clear coat can be done all at one time or more. Their website has a lot of good info. Last but most important is try it on scraps of your woods first regardless what product you choose. Don't get hung up on trying to make every piece of trim and door look exactly the same. If you are uncomfortable with that,go to a cabinet display and look closly at color/tone variance between the parts. The higher the quility,the more variance between pieces that make up the cabinet.

Hey Klem,
Thanks for the good advise. I started the project today. I sanded all the jams and moulding, and used a clear poly semigloss it looks nice and natural. I also pretreated some scrap pine and stained with various shades. The closest match I feel is cherry.
Thanks again,
Chris