Congrats on the new house! Are you moved in yet or at least able to post some photos to get a better idea of what you're working with? The easiest way to update of course is paint. I'm a huge fan of white trim as well and I've painted it at every opportunity. You could also freshen up the walls and leave the trim and casings the natural oak if it's in good condition.

I am stripping mine, which are painted walnut (ew) and painting them white using matte water-based enamel. I've had better results using a small natural wool roller with a soft brush just for the details, rather than just using a brush. I'm just doing trim and doors though, since the floors will go and so will the baseboards, but I am sure it would work for the baseboards if I liked them.