Yeah, those Beofeng's are good to go. Their about the cheapest ham handheld out there, and they have features you'll appreciate. Another good brand, been around a little longer, are the Wouxuns. The Yaesu FT-60R survival has is one of the more reliable and popular ham handhelds, preferred by those suspicious of the unproven newcomers out of China. There are Yahoogroups for each of these where you'll find plenty of support--and you'll probably want that.
With handhelds like these you will be able to communicate widely with the use of repeaters and even repeater networks. Your puny signal coming from a low-power handheld and inferior antenna is picked up by the very sensitive repeater antenna, then re-broadcast at high power by that high-gain antenna so other people with handheld radios with inferior antennas can hear you. You will need to find the frequencies of the repeaters in your area, and know the "offsets" (the transmit frequency paired with the receive frequency) to use them.
Ham radio operators are often very interested in emergency communications ("emcomms"), so repeaters tend to have battery backup and generator backup capability, with hams showing up and watching over the backup power during actual emergencies. In addition, there are "nets" of hams interested in emcomms, where they practice checking in with one another and passing messages ("traffic").
Ham handheld radios can also talk directly to one another ("simplex") rather than going through a repeater ("duplex"); in that mode, the reliable communication range is just a few miles (though certainly farther than GMRS). However, with these radios one can take off the rubber-duckie antenna and hook up better ones (Google "slim jim antenna" or "j-pole antenna" to learn about some relatively portable ones) that can be hung from a tree or the eaves of your house for better range. In simplex mode they'd work great for a team working in the same building, complex, or neighborhood.
Mobile radios (designed to be installed in a vehicle but often used in a base station or made portable with a battery power source) work these same bands and typically operate with more power and better antennas, so again--more range.
The initial Technician Class license also opens the 10-meter band, similar to CB frequencies, and further licenses let you communicate on frequencies that will let you contact people anywhere on earth. Also, you can start right away experimenting with digital voice comms, television, remote control frequencies, text modes such as RTTY, and even interfacing your radio with the Internet and e-mail!
Here's
an article I wrote comparing FRS/GMRS, CB radio, and amateur radio.