There are many homes that have white kitchen cabinets and stained woodwork in them, it really is a personal choice.

Cabinets have nothing to do with woodwork throughout the home. You should keep the look separate!

Do the cabinets first. Probably painting all the trim would be great, but there's no point in doing it if the prospect puts you in a panic, and house disruptions are always stressful enough. If there are clean divisions, you could try doing the trim in the the kitchen, just so that room feels coherent, but honestly, there are people with white cabinets and brown trim who like it that way, so don't feel pressured to bite off more than you can chew. You could always do the trim another year.