Particular models can only retract, or not. Like a Cessna 172 factory made can not retract, unless you physically pay and hire your own mechanic to do it, and get it reFAA certified
Benefits: If you are just starting out as a pilot, obviously the less cockpit controls thebetter. Also for the manufacturers, it would add about $500 to a new airplane, plus all of the programming ro do so.
Manufacturing: Either a model is set with them or not, you CANOT change if it is fixed or retractable.
Piper PA-38-No, you probably will NEVER see one with retractable.
Cost Difference: The only cost dfferences might be because of the increased drag, you burn an extra gallon of fuel... Not a major difference.
Training: I would say fixed gear is better, because obviously, if you are training, you don't want to have to worry about the landing gear, along with all of the others. It really depends if you are training to become an advanced pilot, of your first flights...
Travel: Deffinetly retractable because, usually when you travel long distances, the speed, and altitude is generally higher... along with this comes the factor that the gear could become damaged. So I would prefer retractable...
Sightseeing: Fixed gear because generally for sightseeing, you use slower aircraft..... and have more landing opportunites. So fixed gear would be best, because it is just more widely used, and offers more benefitts.
Transport- Deffinetly retractable... going off of travel, usually transport is flown faster, and higher, needing the retractable gear.
Maintence- Fixed gear is easier because all you have to do is air up tires and you are done, while in retractable you have to do that, along with, checking oil pressure, hydraulic pressure, hydraulic pumps, cheking switches to retract...
-Sincerly
Me