Welcome to the Forum.
Power wise, something between 2hp and 3.5hp will be sufficient.
The more powerful are normally heavier, so something to bear in mind whilst carrying or if fitting at sea.
Standard or short shafted engines are normally suitable.
New outboards are now four stroke engines as 2 stroke have been discontinued due to environmental considerations. 2 stoke may still be purchased second hand.
The disadvantage with 4 stroke is that they can only be laid down in a certain way or oil will get into the engine and immersing totally in water is a no no.
As to fitting, most GRP boats will have a re-enforcing piece of ply glassed into the transom with some extra exterior ply fitted to protect the dinghy from the screw clamps.
Check the rear storage/buoyancy compartment and the re-enforcing panel should be fairly obvious if fitted.
There is no hard and fast rule on which side to fit the engine. Most will choose the side that gives easier access to the throttle/steering arm.
Some disadvantages to fitting on the transom is that the main sheet may get caught on the outboard if using the traveller.
If you do not remove the rudder whilst using the outboard, then the prop and rudder may come into contact.
This does not seem to bother the prop too much but makes a mess of the rudder.
To overcome this, quite a few use an extension bracket for fitting the outboard and can stay there whilst sailing.
Not great for the balance of the dinghy when sailing but it is convenient.
Extension arms are also available for throttle control/steering or make your own from plastic waste pipe.
Some further reading here.
Best to fit a securing cable or rope to the outboard. Accidents happen and you don’t want the outboard left at the bottom of the sea.