From your description and budget, have you considered a cyclocross bike? (I ride both road and CX) but to be honest, you’ll probably get more use out of a cyclocross bike, I know I do, what with winter riding, commuting, off road riding and like you say Sunday morning rides.
You’ve got more options with tires too, you can still stick some fast rolling slick tires on, or something with more grip for winter and off road riding.
If you’re into MTBing, a CX would be a perfect transition to a ‘road biking’ that will still give you a buzz riding on the roads and the option to have a bit of a riot off road and on the trails.
Carbon frames aren’t all that either, most aluminium frames now are lighter and you actually end up going faster and doing further miles on a comfortable bike, as opposed to what it’s made of, unless you’re racing or you’re really hung up on weight, for the price difference, it’s not going to make that much difference.
Disk brakes come as standard on most CX bikes anyway, if your riding mostly on your own or in all weather conditions, hilly areas, around busy towns etc then disk brakes are the way to go.
You’re budget will easily get you a half decent bike for bombing around on.