There are many flavors of Ham Radio... which flavors can be tasted depend upon what level of license is achieved.
For a Technician class license, it's pretty much VHF/UHF privileges (more accurately, the upper half of the 10 meter band and up)
10 and 6 meters offer opportunity for nation-wide communication when conditions are favorable. The higher in frequency you go (2 meters, 70 cemtimeters, etc), the more it becomes short-distance / line-of-sight communications. Wide area repeater systems can extend VHF/UHF coverage for many miles... 100's of miles in some cases. Repeaters with EchoLink (Voice over IP) connections can link to other repeaters regionally or internationally to expand communications to remote locations. If this is the type of ham radio licensing/operating that's in mind, the next question would be handheld? mobile? base?
If handheld, there are many choices under $350. If mobile, also a good number of choices, but factor in the need for a good mobile antenna... that's $50-$75 of the budget. If base, factor in a decent base antenna and a power supply.
For a General or Extra class license, the world of HF radio is opened up. This is relatively low frequency stuff, but offers failry continuous opportunity for world-wide communications. Reasonable gear for HF will probably cost a little more than your target budget, but not too much more.
If you can give us an idea of what type of operation is desired, we can probably make some reasonable suggestions for equipment.