I have a couple of big active dogs, and a couple of underage boys.
I want a floor that will not show too much claw marking or scratches. I thought oil would be the best way to touch things up, especially if I get a rustic type finish.
I worry if one of the dogs has a wet accident will it stain the floor if we have an oil finish?
What would you recommend for the best finish?

A polyurethane top coat will hold up better than an oil based one for high traffic. oil based finishes look better IMO

With both finishes you will to keep grit out,use floor protectors under your furniture, never slide anything across the floor, and have walk off mats at the doorways. It takes getting used to having a wood floor. With either finish there will be maintenance. A smooth film type finish will be easier to maintain by cleaning and re-coating after the finish gets worn, usually 5-10 years. The penetrating oil finish will need more maintenance which you can do by yourself. It is more like a waxed floor. I've had people ask for two coats of finish over the top after few years.