First: the first law of security. You must assume any transmissions you make are monitored. Years ago, when cellphones were plain FM, anybody with a scanner or other radio that tuned to the cellular band - even some UHF TVs - could eavesdrop on cellular phone calls. The industry, instead of installing a dollar or two of encryption hardware in the phones, argued (and won) that the government should make it illegal for you to listen to these calls. The best analogy I can think of is two people come into your house (the radio signals certainly do) and instead of whispering or speaking in code words, get you arrested for listening to them. Don't count on anyone not listening to you because it's not polite or legal.
Practically, that means to keep your communications as brief as possible; it means lower powers are better than higher powers; and it means encryption, which will be the next topic.
For local use, the VHF or UHF (or both) HT is everywhere. I guess that more hams own small HTs than any other style of radio. There are many manufacturers, and as I noted yesterday, a decent rig will cost from the price of a few hundred rounds of FMJ 9mm up. This chart is one dealer's handy way to shop for an HT
You will note a basic single band HT can be had for $89 (about 400 rounds of 9mm FMJ today) and the top end for multi-band is around $500. Note these are new radios, not used gear. Those might start at $25. I have no connection with Gigaparts, other than having bought things from them several times.
What do I own? Currently, Mrs. Graybeard and I each carry a Yaesu VX-6R (our other everyday carry). The combination of features vs. price hits a sweet spot for me, but it may not be right for you. This radio receives everything from the AM Broadcast Band (500 kHz) up to 1 GHz, with the exception of the (hardly used) old US AMPS cellular band at around 925 MHz (the result of that law I mentioned above). This allows the same handheld to be used for shortwave or AM listening, FM broadcast, aviation (should you need that) and two way communications on 144-148 MHz (2 meters), 222-225 MHz (US version) and 420-450 MHz (70 cm) bands. It also allows use of that front LED as a nifty emergency flashlight, too!
It also means that if you're trying to be sure you can communicate with your spouse across town, you should try to put up an outside antenna, as high as you can, and test it out before the SHTF.