Congratulations on going straight to General! Now you've got a lot of options open to you.
Possibly the most important thing you've started collecting is knowledge about radio communications. Knowing what you are doing and what your options are is at least as important as the gear you have.
The gear you get and the antennas you rig all depend on what you are planning for: Total SHTF with bug-in or bug-out plans? Simple regional disasters: region-wide interruption of utilities, etc. due to natural disasters?
Who do you want to communicate with? They'll need the same capability.
First you want 2M capability. All Hams have that. Either a mobile unit or a handheld. That will get you to the local repeaters 10-30 miles away and get you a lot of good info on the local situation. Stick a j-pole antenna on the roof or even in the attic and you'll be surprised what you can do with a 5W HT.
For larger area coverage you'll want an HF +6M rig. That will get you around the world, though as you've learned, it isn't reliable and dependent on the atmospheric conditions.
If you want just one piece of gear, consider something like my Yaesu 857. It covers all the HF bands (100W) as well as 6M and 2M (about 50W). It is designed to be a mobile rig in the car, but works just as well on a desk at home.
You'll want to outfit your family with FRS/GMRS radios and maybe ask some of your important neighbors that don't have Ham licenses to do the same. Don't expect more than a mile range in urban settings. Those 10-20 mile claims are probably between boats over open water.
Also, pick up a CB radio and antenna at the next flea market. When the SHTF you'll want to be able to collect information from as many sources as possible and when communication services have been out for a few days there will be quite a few people dusting off the CBs.
