I can't think of any reason why you would want the trim to overhang the baseboard by 1/4". This is exactly what you would get with 1/2" baseboard and 3/4" trim. Using baseboard and trim of the same thickness is the common practice. Perhaps there's a good reason for using 1/2" thick baseboard, but it is likely to look rather flimsy. Using standard 3/4" for baseboard and trim would seem to be a better plan.

You could use plinth blocks at the bottom of the door(s) and have the casing and baseboard butt up against them. Make the blocks have enough of a "reveal" around the casing that they should eliminate the gap. This is really the only solution when the casing has a complex profile and would meet the baseboard at a corner, unless you have some way of cutting/routing the "negative" of the casing's profile.

I think you can and should do the taller baseboard molding. It will look better than small. We are doing ours right now too and I have the same issue. I am actually doing a 5”. baseboard.

@StarCraft Reviews Thank you! After watching the video, I'm assuming using flat casing vs. colonial style would look better since there are no lines to match up after cutting the one side to fit. We opened up a wall between the dining room and kitchen and I'm planning on having crown molding put above the kitchen cabinets. Since the rooms look into each other is it best to keep the kitchen crown molding the same as what is already in the dining room? I like the cleaner look of the flat base/casing with my new doors but don't want it too contemporary or too trendy. Seems like much of the newer homes and remodels are using the craftsman trim as it blends with lots of styles. Here's my doors.