At that budget you can and should get a top shelf bicycle. There are endless options in that range. If you are serious about getting more into cycling, I'd suggest skipping the middle and go straight to a high end bike. It will be cheaper in the long run, IMO. Once you get into that range there really isn't going to be any reason you can't keep up with people on carbon bikes. The difference will be trivial as compared to fitness, which is really about 99% of it.
I suggest looking for a vintage road bike with Columbus SL/SP, Reynolds 531, Tange 1/2/Prestige, or Ishiwata 022. Realistically these will all perform about the same. I realize I just contradicted what @
noglider said, but it's not a bad first filter in picking a bike. When you have some candidates, then start looking at geometry. For general recreational use, an audax or old style road geometry is a good bet. 73º parallel, neutral trail, reasonably long chainstays. Size and TT length that are right for
you. The Competive Cyclist fit calculator works really well. I fit people professionally for years, and I used it on myself when I got a custom bike. It spit out exactly what I had come to find worked best for me over decades of riding.
What I'm saying is figure out what size you need
first, then start hitting Craiglist, the for sale board here, ebay, whatever. There really are endless options. You might narrow it down a bit by deciding if you want to go Italian, English, French, Japanese, American, or other.
When you are at that point, then start thinking about components. Can't go wrong with Campy NR/SR, or Superbe, or Dura Ace 7400 or later, or Ultegra tri color, or a mix of good parts. Don't rule out old Frenchie stuff either. It can be more of a hassle to work with, but it's right up there.
Yeah, there are lower and midrange steel bikes that ride nice, but in Los Angeles, lighter is better. You will probably be riding up and down hills
most of the time, whether you're doing trash truck or the climbs in the San Gabriels. This is no place for a UO8.