I'm in the same boat, got sick of stress related injuries and figured I'd give cycling a try as just something new after running for a couple years. At this point, I've got a good bit of advice that I hope can be useful.
As far as a bike, realize that not all carbon frames are made the same. You can buy some carbon Fuji for 750 or around there which is definitely not comparable to a carbon frame 10x the price.
Aluminum can be a very smart way to go, especially models of the last 3 years or so, particularly Cannondale's CAAD line or Specialized's Allez line. Both have really remarkable performance for the price point, compared to carbon.
As far as components, anything new at this point for road bikes are 2x11 speed, but honestly, 2x10 speed has become so cheap without really being outdated that it's the best way to go, in my opinion. If you're looking to put in some training miles on this though, do what you can to not go below a bike spec'd with Shimano 105 or Sram Apex, and it's okay if it's a couple years old. At that level, the components hold their shape pretty well over a couple years.
Riding in a group is definitely one of, if not the best part of cycling. You can go so fast and go so far unlike any other sport. A 60 mile ride in a group will feel like it takes the same energy as doing a 35 mile solo ride. Group ettiquette is very important to learn and the group will take every chance it can to be elitist and tell you to get out of the way in a group. If you can find a group ride in the area, just sit on the back and get comfortable following wheels for a couple rides and watch the movement in the bunch. Whatever you do, don't get discouraged because it literally takes everybody a while to get used to it, it's not a natural thing at all.
Last thing I can tell you about the sport is that compared to my experience with running, things are so much more tangible. I ran XC and Track, and between mileage runs, the workouts and the races, everything felt... arbitrary in a way. In a race, you win if youre leading at the end of four laps. You run around a golf course in some stupid loops until you run exactly 5000 meters. But in cycling, you climb up the mountain, and you don't get to just jog it in, you have to climb the whole thing, and you stop when the mountain stops. It's not something easy to explain on a letsrun forum, but it's very refreshing compared to running, and it's not something I ever realized that bothered me about running. I love both sports, but for now I've been cycling.
Hope that everything goes well getting into it. I'd be happy to answer any questions if you somehow have any more after reading this novel. Good luck.