With lighting, like cameras, there is no one right solution.
Personally, I like to travel light, and with interiors I always like to make use of the existing light, sometimes to reveal the lighting design itself, but also to capture a mood, a sense of the space as it is, not how I
can make it, and then I help it out, with....
Several cases loaded with a large variety of tungsten lights.
Multiple cases of strobes (Comet) 2400ws and 1200ws (some bi-voltage) - for spaces predominantly daylit.
BUT I always start with the existing light. I admit, that can take some planning because different times of day will provide dramatically different light in a space, but that's the way I see it.
I should add that I do a fair amount of layering of various exposures to produce each shot. Ah, the beauty of shooting digitally!
Other photogs I know will choose to re-light the entire space, others will use HMI's, still others, for speed, will shoot available light only and layer. There's no right or wrong, just a particular style of shooting.
Trying to decide which lighting to use to shoot a particular space comes with time and experience. As I said, it's good to actually see how others do their work (workshops). Some solutions you'll like and adopt, others not. Your style will evolve. Mine certainly did.
To answer your last question, "Are you doing alot in post with color management?" The problems you don't solve while shooting, you have to solve in post. So the broader your knowledge of lighting technique becomes, the easier post production will be.
One last thing for you to think about with architecture, concise composition.
Hope this helps.
how are you guys lighting, I've heard of several different techniques, one of my main issues is getting those crisp whites without getting too yellowish, and overpowering my strobes. Are you doing alot in post with color management?