We remodeled our kitchen last year (after 16 years of living with ugly particleboard and faux butcher block countertops). I had years and years to discover what worked and what I'd change.
I can tell you that choosing cabinet styles was the most time consuming part because my hubby and I had a slightly different vision. Like you, I didn't want grooves and moldings that got dusty, nor did I think modern, flat-faced cabinets fit the style of our home. On top of that, we don't plan to be here more than a couple more years, so we weren't going to make upgrades like putting on glazes and such. We both love cherry wood, so that was a given, and we searched till we found a stain we both love. We also found a door style that has only one overlay. Easy to clean.
Trying to redo your old cabinets could be a bigger problem than replacing them. I've seen some done well, and I've seen some really tacky ones. Since cabinets are the focal point of the kitchen, I say replace them all.
As for the hidden trash that the dog couldn't get to, it was among the top 3 things I HAD to have in my kitchen. (Roll out pantry shelves and more drawers throughout were the other two.) I wanted the trash where I could open a pull-out cabinet and simply swoosh and drop trash into it as I cooked or cleaned. BEST DECISION ever. Ours actually has 2 bins--one for trash, the other for recycling. (Our state has streamlined recycling, so I don't even have to sort it.) It's not sexy to think that the hidden trash is about my favorite thing, but I smile inside every time I pull it out.
My dog thinks it was the biggest disappointment.