You have a home (a lovely home) with many warm toned features - all the trim, cabinets, paneled doors, kitchen cabinets and it looks like some built-in in the family room. You can go with a white / cream or any warm tone (even green and some blues) kitchen, but to attempt the currently popular white gray cool colors trend would mean a whole house transformation - expensive, and potentially in need of an update again when the trends change - and since this trend has been going strong for about 5 years in my area, I give it another 5 to 10 years at a max. Actually had a cabinet person tell me lately that they were pretty tired of it now.

A white kitchen is more timeless and can with more ease be blended into what you have now and move more easily into future changes. You may want to do a white/wood look in your home which is a blend I have in my own home. It keeps the warmth of wood but also the brightness of the white and makes it possible to use both elements when wanted. For example, I have white trim, but wood paneled doors. My kitchen cabinets are wood and so are three bathroom vanities. My powder room vanity is white and so are my laundry room cabinets. I painted a dark bookcase white, but kept the fireplace mantels wood. If you do a gray island, look to one with some blue undertones to better work with tans, creams and light beiges.

Yes - I think shelves in place of the cabinets over the desk is a good idea.

Mixing wood and white:

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I wanted to add some more to my prevous comment. Oak is not a paint grade wood. This is because the texture of the grain shows through the paint. Many people paint it anyway and are very happy with the results - others are disapointed. Also. DIY painting of cabinets is a difficult and time consuming task. It takes a patient and experienced DIY person, so we usually recommend that cabinet painting be done by a professional painter. Whether done DIY or by a professional, painted over cabinets do not have as durable a finish as factory painted cabinets. This is not to disuade you from paintig the cabinets, but to go into it with the facts.

Your wood paneled doors should probably not be painted. Wood moves with changes in temp and humidity and this cracks the paint at the joints and doors have lots of joints. This will happen to your cabinets too so some touch up will be necessary - or not because it will just crack again. This is why most factory painted cabinets are MDF or MDF combined with wood (usually maple). The MDF is more stable to temperature changes. You will see many people online very happy with their painted cabinets - most of these have a farmhouse type style where a little chippyness is OK.

Some other options are to reface the cabinets including new doors - a little expensive and probably more expensive then painting. You can do something like the first picture posted where uppers are replaced and the soffit removed - with or without new doors for the lower cabinets - again a bit expensive. You can update keeping the cabinets wood - you might have to change your vision a bit as wood cabinets lend themselves to more rustic / country styles than contemporary. You could do this while still paintin the trim white. You can quit watching HGTV and stay off Houzz with the result that you will probably grow to like your own kitchen more - probably the cheapest option:)

My kitchen is oak and in my "my pics" idea book - it is not contemporary, it is cottage / French country, and recently "refreshed". I get inspiration from European cottage kitchens where the cabinets themselves are often no big deal but the decor sets the tone.

This is really great advice. I think i will leave the wood doors alone. I'm looking for the most economical option to update the kitchen, so we decided to go with paint. We will budget for an overhaul in the future. We took a trip to Sherwin Williams yesterday and narrowed down some colors.

I'm still on the fence about white trim throughout.

Here are some examples of painted kitchens with wood trim. If you keep or bring in some wood elements it can work well:

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Putting together a kitchen color palette can be challenging!
Here is a great article that might help: Kitchen
Color Palette