What aircraft design elements contribute the most to sustained flight?
Natural stability would be highest on the list for me. Look at free flying model airplanes for inspiration. They have their own characteristics:


Very low wing loading for minimum sink speed
High natural stability, and consequently a very narrow speed range
High aspect ratio wing, thin airfoil with high camber
Extremely short fuselage ahead of the wing (no payload to carry)
Extreme fuselage length aft of the wing which provides ample aerodynamic damping
Strong dihedral of the outer wing.


This in combination means that your control software can be very simple. Relaxed stability will require many sensors and built-in redundancy, and the more parts you need to add, the more possibilities of failures you will end up with. In contrast to that, the laws of physics never fail, use them to your advantage. See below for an example which I copied from the Wikipedia page on free flight models:



For airfols, c.g. location and all other details I recommend to look at several free plans until you see a common pattern.

Regarding the type of fuel: Depends how noisy and messy you tolerate the engine to be; some people will only fly electric while others are happy with two-stroke engines.