Not really, it is very dependent upon the circuit and application, though there are optimal choices in some cases. Devices are just devices, they are not in themselves designed for different purposes. You can use a FET or a BJT as an output or input device, just have to decide which set of trades is correct for your design. High-impedance inputs made be better served by (J)FETs, which do not require base current, but in some applications a micropower BJT circuit is a better choice, say lower input impedance requirements and higher gain. High-power switches (such as required for class D outputs) are often FETs of some flavor due to their low "on" resistance, no BJT Vbe drop, and limited drive power when static (they need power when switching, but almost nil when static). You can use cascoded FETs to provide high gain since you can stack them repeatedly as a current source to increase their output impedance, unlike BJTs that have limited output impedance due to base current, but you need the headroom to stack them.Being that they are devices for different purposes, is there a rule of thumb for which kind of transistor should go where?
The things you are asking are again the sort of things hard to explain in a few forum posts. Circuit design can take a lifetime to master.