I lived in my house (built in the 60's) for several years before re-doing the kitchen. It also had builder's grade, but from the 1960's, LOL. My ex was against any of my ideas, which is one of the reasons he's an ex, and I waited until he was gone.
I had worse cabinets that the prior owner had painted blue. There is no detail on them with framing or molding, just flat doors. The style of kitchen you are talking about is similar to what I ultimately wanted, and have had to scrimp and save for. I've done a lot, but a little at a time. I also had very ugly light brown tile backsplashes that I painted white as well with a higher gloss paint, no problems, and it's been about 12 years.
YES, you can paint wooden cabinets. Tarheel's look is wonderful. I painted the outside and doors white. What I did in my kitchen for some of the overhead cabinets is take the doors off, paint the inside of the cabinet white and use them with baskets (for baking goods), or like a china cabinet top with crystal in them. I think I left the doors off about half of the cabinets. I found fabric gingham contact paper and put it on the bottom of the door-less cabinets, with a slight overhang onto the cabinet facing bottom, so it looks a bit "French/country chic/Americana".
I will be building a corner nook with a longer country styled table, and chairs on the side opposite the built in bench. At one of the short ends I'm going to get bookcase and small desk from Ikea (or build them) so I have more shelving and a place to store paperwork. I have tons of cook books and don't mind an open storage look.
Don't let people criticize your ideas. Start small, with one door maybe. Sand and paint carefully after priming. You can have what you want, and it doesn't cost that much.
Also, it is possible to buy custom doors only. Google "custom replacement kitchen cabinet doors". You can get them with glass inserts or anything else you like to supplement what you are doing. I have 19 cabinet doors and multiple drawer fronts, and when I priced this out several years ago it was less than $800. If the cabinet bases themselves are solid, this is often a good option. Especially if you don't mind the floorplan/layout of your kitchen.
As for colors, I'd recommend getting those small sample sized paint jars from the home improvement stores with some colors you like and painting an area when you are ready to start.....helps you to avoid "mistakes" later.
My motto in life: There's nothing I can't do, only things I haven't tried. Take your time making decisions and you won't regret what you try.