Welcome. As you are finding, being older does not mean you can't improve your fitness and endurance.
$1,000 to $1,200 should get you into a really decent bike, probably with a Sora or Tiagra group set. Nothing at all wrong with those.
Find a good shop where they will take the time to ensure a good fit, and back the bike up with service, and the name on the head badge won't matter a whole lot.