ISO and ambient lighting

I shoot "for sale" homes for a real estate company for them to post. I have my camera set on program (Canon 60D) and not too concern about professional quality, but it wouldn't hurt if I can achieve it. Generally, I shoot about 150 photos per home, depending on size. I'm still uncertain how to set the ISO to achieve a proper balance of lighting. Outside photos are usually OK but I have noticed some darker photos on occasion. Inside photos are the problem. Some rooms may be darker than others and if I use flash, I occasionally get white wash and if I don't use flash, the shutter speed is slow enough where my movement will cause blur. Basically, many photos are far from professional quality, but good enough to post.

How do I achieve the right balance and closer to pro quality?

In a word: tripod.

Trip the camera's shutter release with the camera's timer or a separate trigger. It's not the only solution, but in your situation I think it's the simplest. Set your ISO as low as possible, set your f-stop at a higher number for greater depth of field (5.6, 8, et seq.), and set your shutter speed as slow as necessary to achieve proper exposure. There are a number of techniques and choices that come into play, but they range from basic to advanced levels of understanding.

Because of the differences in light inside the house vs outside, your best bet is HDR (High Dynamic Range)

Take 1/2 the exposures based on the outside lighting (assuming theres windows) and 1/2 exposed for the indoor light.

Some cameras do the work in camera - yours may require a little PP.

I think the latest version of DPP does HDR as well.