I agree with Larry about the cosmetic issues of removing the bank of uppers above the stove. But perhaps you're really handy or know someone who can deal with the aftermath? On the other hand I'm 100% for removing them (carefully). They interfere with the sightline from one room to the other and will create a more current, open concept look you seem to want here. PS: if you are going stainless consider changing out all the black hardware for something stainless matching. Nothing too modern tho as your style of cabinetry is vintage 50s/country vibe. Otherwise the black hardware may look odd once all the black appliances are gone. Then paint the inside of your door pictured a taupe/gray to match your countertop - thereby tying the whole thing together. Post some after pics too. Cheers.

Yes, remove all, of the cabinets. There is a much better layout to be had with much better quality cabinets. Ones with actual usable drawers and adjustable shelving. Start with a KD to help you plan the renovation or you'll just end up wasting money with no real changes.