Picking a juicer really depends on how much you plan on juicing. Hand juicers are fine for home use and cocktails to order but most bars need the help of something a bit more industrial. Check my post about different juicers here.
I don't recommend juicing anything a la minute. every different piece of produce you juice will have different sugar and acid content. Also depending on the pulp in your juice and how you strain the cocktail, you could be getting wildly different yields. juicing in large batches and straining allows for greater consistency over the course of the shift. Some people like the pageantry of seeing the fresh juice squeezed in front of them but it does lead to less consistency overall.
Fresh juice has a fairly narrow window for their ideal flavor. Lemons, limes, and grapefruit are delicious freshly juiced but many people think they get even more flavorful after a few hours of rest and are good up to 2 days (48 hours) later. The shelf life of oranges is a bit less forgiving. Oranges contain substances called lactones, which after juicing, develop into limonin which has a bitter flavor. Fresh is best wish oranges but you can use it up to 4 hours after without much issue.
This theory is odd. People think that the fruit sacks or cells are scrunched together and warming them up will ease the process of juicing. Some people even think that microwaving the fruit will make it possible to extract more juice. Don't do that. Everyone who has tested this has disproven this concept. The yields are the same regardless.
Myth: Rolling the citrus yields more juice.
This is the same silly idea. Even Jamie Oliver thought this works. No, it doesn't. People have tested it. Don't waste your time. A good press juicer extracts all the juice possible, you're not manifesting new juice.