Some useful resources:
Those are all good resources for learning. DIY drones sells stuff too but it has a useful forum section.
In short: 3-6 miles can fairly easily be accomplished with electric. Your first FPV/UAV project NEEDS to be electric. The vibrations and engine tuning and throttle management issues and limited information on making IC engines work with autopilots make it especially challenging. It can be done and it can be done well - just don't start with it.
Get all your FPV/UAV stuff from a vendor with a great reputation - go cheap and you will be buying it twice.
There is so much info - start combing through the links above. Read the sticky section(s) on the RCG link I gave.
Oh and you CAN accomplish your goal on your budget if you hold off on buying and gorge your brain on reading from the above links (and others you will find along the way).