J.J.
I completely understand your situation - my parents are moving here with me soon. I agree, start with internal/family medicine and get referrals from them. Baylor Grapevine is a great hospital (I work there) - but if you have speciality needs you may need to go to a larger hospital downtown (my mom needs a specialty neurologist, and oncologist - my dad needs a really good cardiologist and cardiovascular surgeon). Eye doctors, dentists, etc. - it can feel overwhelming!
BREATHE - as long as they don't have immediate needs, you will get it figured out.