You have a couple of different subjects going here:
1. It is possible, and legal, to "listen" to military communications. It is a popular hobby with many people. Check this web site for some ideas:
Military Comms Monitoring. HF VHF UHF Do a Google for "monitor military radio," etc. for more sources.
2. If you want to "listen" the easiest way is with some research, like the above web site, and an inexpensive scanner.
3. If you want to listen using something military, any of the VRC-12 family radios (including the PRC-25 or PRC-77) will work if you know the frequencies that are in use. If you don't know the freqs, then research, time and patience .. and a scanner will help. If $$ arent' an issue you can buy some of the SINCGARS equipment that is being replaced by new gear.
4. Anything in the frequency hopping or encrypted mode is off limits.
5. Communicating using the various military radios is possible, with a ham license, and only in a limited range of frequencies. Check the ARRL web site for more details. A Technician (lowest class of license) is easy to get and would allow use of the appropriate frequencies using military gear.
Hope that helps to clarify things a bit.