In an ongoing game, you can find these statistics by clicking on Reports -> Help -> Planet statistics overview. At the bottom of that screen you can also find what kind of airplane engine your secretary recommends to use on your planet.

Gravity
Affects the weight calculations of the aircraft, reduces speed and range. You generally want lower gravity for better aircraft, but higher gravity planets tend to also have thicker atmosphere to balance it out.

Air pressure
Decreases speed, but also increases range. It seems that a thicker atmosphere is generally better for aircraft and will be a big factor on determining the range.
The air pressure also determines the speed of sound, which acts as a speed cap for non-supersonic aircraft. The thicker the atmosphere, the higher is the speed of sound.
Rocket engines are special in that they are the only engine type that actually increases range the lighter the atomsphere is. If there is no air pressure at all, aircraft require rocket engines to fly.
Thopters are better when the air pressure percentage (in relation to Earth's) is higher than the gravity.

Airplanes - Ultralight, Light, Medium (1 and 2 engines), Heavy (2 and 4 engines), X-Heavy (4 and 6 engines)
Helicopters - Light, Medium, Heavy
Thopters - Light, Medium, Heavy
Helicopters, thopters and airplanes with VTOL engines can land anywhere, but at a reduction of their max readiness. All other airplanes require airbases of increasing sizes.

Role
The role determines if your aircraft should flee from air combat as fast as possible and if it should be flying low or high.
Flying low gives better recon, flying high gives less accuracy, but also generally makes it harder to be hit by AA.

Engines
Bigger engines increase speed (up to the speed cap), but they are also less weight efficient and less fuel efficient. If the aircraft is already at the speed cap, there's probably no benefit to increasing the engine size.
VTOL engines allow planes to land anywhere at a readiness penalty.
Helicopters only use rotors.
Rocket engines are required without air pressure.

Wings
Bigger wings increase dogfighting score, range, max weight and reduce minimum takeoff speed, but also reduce the aerodynamics and increase weight.
This means that wings both increase and decrease dogfighting score and I'm not sure if higher speed or bigger wings are better for dogfighting.
Helicopters don't get to choose.

Fuel Tank
Bigger fuel tanks increase range, but also increase weight. Adding a fuel tank that is too big might give no benefit besides reducing range.

Air-to-Air Weapon
Machineguns (mounted and cupolas) give a big malus to the first 2 rounds of air combat.
Mounted machineguns can also be used for anti-surface combat.
MG cupolas can only be used by heavy and extra heavy airplanes and are strictly for air combat.
Air-to-air missiles have the same firepower against surface targets as MGs, but are vastly more powerful against air targets. They are unlocked by the Missiles tech.

Air-to-Surface Weapon
Bombing hatch + bomb are good against structures and soft targets and also give you cargo space, letting you use the bomber in potential air bridges.
Precision bombs have double the fire power of hatch bombs and are better against hard targets. They can't be used by helicopters, nor by heavy or extra heavy airplanes.
Air-to-surface rockets are unlocked with the Rocketry tech. Can only be loaded by light and medium airplanes, helicopters, and thopters.

Cargo Space
Necessary for air bridge missions, but increases weight.
100 kg of cargo space translate into 1 logistics point, but it also gets multiplied by the amount of aircraft in the formation.
The maximum size of a unit model that can be transported via air bridge is the square root of the bridge's average capacity divided by 1000. (For example, if you have an air bridge consisting of aircraft that each can transport 1000 kg, then the maximum size is the square root of 1 -> 1. That would mean only infantry could be airlifted by this bridge. If the average capacity was 4000 it would be the square root of 4 -> 2, which would let you also airlift transport trucks.)

Most of these stats are influenced by the planet's gravity and air pressure.

Hitpoints
Increased by size and by the Aircraft Rugedness optimisation technology.
Size
Increases hitpoints and the square root of the size determines how many airbase points the aircraft needs for full readiness recovery.
Weight
More weight means less range, less speed and higher minimum takeoff speed.
Speed
More speed means more range and better dogfighting score.
Influenced by engine power, weight, aerodynamics. Capped by air pressure for non-supersonic aircraft.
Minimum takeoff speed
The speed needed for the aircraft to take off.
Influenced by weight, wings, maybe engine?
Range
Range determines how far the aircraft can fly. It's translated from km into hexes by dividing it by 200.
Influenced by weight, speed, wing size, fuel tank.
Operational range is the range aircraft can fly missions at and it's half of the maximum range.
Because of the way range is translated into AP movement cost, the amount of hexes for operational range can only be one of these numbers:
0-12 at 0-2400 km
14 at 2800 km
16 at 3200 km
20 at 4000 km
25 at 5000 km
33 at 6600 km
That means, if you design an aircraft that has a range of 6000 km, it will still only have the same actual hex range of an airplane with a range of 5000 km (25 hexes). Only at 6600 km the range will jump over to 33 hexes. So, you should be aiming for these specific km numbers when designing aircraft, or you're essentially wasting engine power or weight.
Dogfighting score
Having a higher dogfighting score than the enemy planes in air combat will give you a bonus and the enemy a malus.
Influenced by speed, wing size and horsepower to weight ratio.

Aircraft/ Helicopter/ Thopter Design - These increase the structural design value of newly designed aircraft model serieses of the corresponding type. "Aircraft" Design only applies to airplanes, despite the name.
Propeller/ Jet/ Rocket Engine Efficiency - These improve the fuel efficiency of the corresponding engine type. Helicopters use Propeller Engine Efficiency. The normal Fuel Efficiency tech also applies to aircraft.
Leightweight Alloys - Reduces the weight of your aircraft designs.
Aerodynamics Design - Improves the aerodynamics of your aircraft designs.
Aircraft Rugedness - Increases the hitpoints of your aircraft designs.
Rocketry - Lets you put air-to-surface rockets on your aircraft.
Missiles - Lets you put air-to-air missiles on your aircraft.

ENGINE EFF - Fuel efficiency of the engine
HP:WEG - Horsepower to weight ratio
AERO - Aerodynamics
OP RANGE - Operational range in hexes
FIREP - Firepower
Rnd 1, Rnd 2 - Round 1 and 2 combat modifiers

Vic has shared a useful document showing what kind of aircraft ranges you can expect on planets with certain gravity and air pressure values (on version 1.05 beta 19):

http://www.vrdesigns.net/openbeta/analytics_air.pdf
https://www.matrixgames.com/forums/upfiles/12041/1C65967AE42B421D94F44F498B3AC0D4.jpg