Yes, you are talking about a drone, not an RC plane. You asked about something that could go a few miles round trip. That would put you into commercial drone territory. You say you want to do this on a fairly tight budget. If around $5,000 is what you consider fairly tight, it's doable. But it sounds like you are looking for something more hobby grade with a hobby grade price. The various 450 size quadcopters can carry a good camera (Mobius, GoPro, etc) along with FPV gear and enough batteries for a 20 minute flight or so. There are folding ones on the market that would pack small and give you around 5 pounds to stuff into your backpack. Range will be around 3/4 mile from the launch location before the video signal starts to go away. Around $1000 will get you a GPS equipped drone with waypoint navigation and the electronics and batteries.