Both landlines and cell towers have limited battery back up, some have generators. At any rate they will function for a while during a power outage. So having a plain land line phone for at least ONE of your house phones is a great idea. So is having a car charger or other way to keep your cell phone working from your end.
All of the following come in hand held [walkie-talkies or handi-talkies ] vehicle mounted and home / base stations. The difference in configuration has nothing to do with the frequencies that they work on.
FRS / GRMS are ok for very close range. They are no more ‘secure’ than any other radio except for the very limited range. These would do well for a highly populated / dense area such as New Your City.
HAM radio is a great idea too. Talking around the block or around the world! They can be very expensive or really economical depending on what bells and whistles you want. With a license you can work on low power, 1/2 watt units clear up to 1,500 watts on the same frequencies. There is one multiband radio that I would like to have a couple of. It is man-packable, has an internal battery or can hook up to any 12 volt power source, the antenna can be rolled on to a spool, it works on 160 meter band all the way down to 70CM. This is an extremely wide range for a single radio. With this radio you can talk clearly around the world. I have heard folks talking from Scotland to New Zealand. The maximum wattage that it has to transmit on is 5 [five] watts. Each of the  levels of license for HAMs are cheap – So for easily less than $100.00 you could have all 3 levels of licenses. Google ‘HAM radio club’ to find a group near you to help you get licensed and set up with a radio to start out.
Not everyone in a given area of operation or group needs a HAM radio. In fact it is a good idea to NOT have everyone in a group area on HAM radio. One of the problems with everyone working on the same radio frequencies is confusion. Think of it as the old ‘party lines’ back in the days when the phone systems had a group of people on the same phone line. If 10 people had to share the same phone, you can imagine if they ALL talked at the same time. Now, hold that thought and think of the party game called ‘telephone’ where you have a simple message written down on a piece of paper. You whisper that message to the first person who then tells it to the next and on down the line until they get to the last person who tells the group what he got told. You will not recognize it.
Another issue is that in any group there are a bunch of conversations going on that are not ‘private’ but at the same time does not pertain to everybody….. sort of like when you are on a yahoo group site. The nice thing about cross talking or party lines is that if you have something to add you can jump in and say whatever.