How did you come up with that budget? Seems like a lot for someone just getting back into it. My wife had similar ambitions a few years ago and she ended up going with an aluminum 105. I'd be surprised if she's ridden it 200 miles total. I was prepared to drop $3,500+ on a nice bike, but in hindsight I'm glad we didn't go that route. You can always get a nicer bike later and keep the starter bike as a backup/rain bike. All the specific recommendations you'll get are really just personal preferences, and it's impossible to know what your personal preferences are until you spend a bunch of time in the saddle. A hundred mile day is around six hours in the saddle give-or-take so it doesn't really require anything special. I do a lot of randonneuring, and the equipment choices that group makes are quite different than what you'll see on the typical group ride.