No matter what you stain it with any cut marks will cut through it and show the lighter wood under it. I would give it two months of daily mineral oil soakings and enjoy it for what it is. You'll want to maintain the mineral oil once a month after the daily applications so it doesn't dry out again. You'll also see the cracks get much better as the wood gets healthy. Use of bees wax to fill it will not work. The wood will absorb all oils out of the wax causing the wax to shrink and just look nasty.

The bar I would finish with PURE tung oil it is food safe and also gives a really lovely finish and because this is a beach house I would use the same on the mantle and I would have them both darker.

A natural finish is a classic look for oak floors. It will blend with the cabinets you have now and look great with your white cabinets later. It also is the best color for camouflaging scratches and dust. It goes with almost any paint color. If you stain dark, there is no going back. Once stain gets into the grain of oak, it is very difficult to impossible to remove and you will not be able to refinish it back to natural.

A couple of thoughts: I would move forward with replacing the ovens and cooktop - with stainless - it will create a cohesive look with all appliances being stainless. A new owner could use all the appliances if they redo the kitchen. Before spending any money on painting cabinets, new counters or a backsplash. Go look at photos of homes that are for sale in your neighborhood. If your already working with an agent to find your new home, ask them if a redo will make a difference in your sale. At certain price points people may or may not have money to remodel a kitchen. For a buyer that can't afford to remodel, having an updated kitchen could sell your home. Cabinets: DON'T paint them yourself. Spend the money and hirer a professional with good references and ask to see their work. I have sold a number of homes over the years with DYI paint jobs, they never look professional and most people skip the proper preparation techniques and the paint doesn't adhere properly. The last couple of homes I sold with Corian counters - we offered an allowance to the new buyers (set a price limit and have a local stone yard preselected) If your going to stay for a while - do somethings you will enjoy, but with resale in mind. If you don't mind the cabinets, replace the counters and install the backsplash. A light colored counter and backsplash will brighten up the room. Also if you replace the counters, install an under mount sink. Even if you do nothing add under and over cabinet lights -it will brighten the room. Easy weekend project to install . You already have electrical to plug into from the microwave and behind the fridge. (There should be a gap between your cabinets to run the wires) - use the warm white LED lights and you can install a remote controller (like the one for holiday lights w a remote) behind the fridge and in the cabinet. Easy on and off.