Further to Silvaire's useful information;
If the aircraft you're flying has an "encoder", there should be a placard somewhere on the instrument panel, or face of the altimeter, saying so. If you find such a placard, you can assume that "ALT" will transmit your altitude corrected to 29.92", along with the transponder return. This has no direct benefit you you, but all kinds of benefit for others.
If you blunder into someone's controlled airspace, whoever is watching radar there can see you, and your altitude, and at least keep everyone else away from that #*#^ airplane.
In other airspace, those aircraft equipped with TCAS will see your altitude, and again, be able to separate themselves from you, even if you never know they are there.
Unless you are deliberately flying at an altitude you should not, and want to conceal this fact, operate in altitude mode.
If you cannot find the aforementioned placard, assume no encoder is equipped. Then "ON" and "ALT" have the same function.
If you have a total comm radio failure, select 7600 (well in North America, anyway). This will tell radar controllers that you've had a comm failure. Continue flying to where you have been cleared, if in controlled airspace, or leave controlled airspace my the least intrusive route.
If you have an emergency, for which "Mayday" is appropriate, select 7700. You'll get a lot on attention, much of which you'll never know about. If you're also squawking altitude, and you go down, radar will know that you have, which is what you want.
If in doubt, while flying in radar served controlled airspace, ask the controller what they would like you to do with the transponder.
My modest, non expert, understanding of the warm up for transponders, is that most have something inside known as "the cavity". It has properties similar to a vacuum tube, and warming up and cooling down are good things for it. A few minutes of each will do no harm.