A real easy way to play/listen is to purchase an RTL-SDR. $25 and you can listen to most everything around you, including HF. Look up ARRL amateur radio band chart for Freq ranges.
Check out repeaterbook.com for a listing of repeaters in your area. For a cheap vhf/uhf hand held you can't go wrong with a baofeng uv5r to learn on.
Another suggestion, google around to see if there's a local amateur radio club around you. Field day is coming up this Sat, if your local club is participating it would be an excellent function to attend and a perfect time to get on a mic.