What are the factors considered while placing a propeller on a plane?
The biggest factor is familiarity: What has worked before?

Other factors are:


Propeller size: Slow-turning propellers driven by powerful engines have a big diameter. This is desirable because it improves efficiency. However, now the propeller cannot be placed behind the wheels if the rotation angle should not be restricted.
Engine location: Driveshafts cost weight and run the risk of resonance problems, so the propeller should be directly in front or at the back of the engine. The engine location is dictated by the desired mass distribution, cooling, the pilot's field of vision, and space demands.
Interference: This includes all factors like prop wash and swirl. Putting the propeller ahead of control surfaces or flaps improves their effectiveness at low speed. Conversely, the increased flow speed increases friction drag on the surfaces wetted by the propeller's slipstream.
Stability: The propeller acts like an additional small wing and creates lift and side force when not exactly perpendicular to the inflowing air.
Engine-out performance: Multi-engined aircraft should still be flyable with one dead engine. This is an interaction between propeller location and control surfaces, and to minimize drag, those control surfaces should be as small as possible. Thus, the propeller should be close to the center of gravity.


The rear propeller is more efficient, because it helps to prevent separation on the surfaces ahead of it, and its slipstream will not increase the friction drag. However, integrating a propeller at the back of an aircraft is hard, so few designs (apart from those in this answer) made use of it. Notable examples are:


A range of British fighters during the early years of WW I, when only the Germans had mastered the technology of synchronized machine guns.
The Zeppelin airships. Their gondolas had rear-mounted propellers.
The Convair B-36. The pusher location in the wing was selected for better efficiency, but created cooling problems for the engines.
The Learfan, started during the first oil shock and designed for efficiency. Two PT-6 drove a single pusher propeller.
The Piaggio P-180 Avanti, which was designed a few years later and much for the same reason as the Learfan.


Also, Claude Dornier had used two engines in one engine pod, driving a propeller each at the front and at the back, as early as 1915, when he worked for Zeppelin on a giant metal flying boat. This became a common theme on many Dornier aircraft, especially the flying boats, and on the Zeppelin Staaken giant bombers. The last example of this range is the Dornier Seastar, designed in the late 1970s.