Welcome to the wonderful world of brass! Asianeuph is right on point. If you have any questions about more specific details I'd be happy to send pictures to help explain this better. You can probably find a good used trumpet for not too much a couple hundred? The director should be a good help in the care department of each specific instrument, but here are some general care tips.
I'm going to just go a straight forward as possible so I don't miss something. Some of this may be similar to caring for you flute physically.
Oiling: it doesn't take much oil to keep the valves moving smoothly when they are clean, just a drop or two a day just to keep it moist. Using any of the above mentioned oils. Most local stores only sell the 2oz applicator bottles, the 8oz bottles will last you a while!
Slide lube/grease: again, doesn't take much especially for trumpets. Just put a little of the grease on the slide and spread it around with your finger and then push the slide closed, and then wipe off the excess.
Exterior metal cleaning/polishing: actual polishing using compound is not necessary on a regular basis, but a soft rag/cloth to wipe off waster marks from emptying the spit valves or something of the sort. Lacquer instruments can be polished from time to time with a lacquer cloth, and silver plated with a silver polish cloth. Excess polishing can wear down the finish faster than normal. Untreated cloth cleaning is fine, but cloths with compound will wear down the finish faster.
Bathing: for lacquer instruments especially!!! DO NOT USE HOT WATER. It will take of the lacquer finish and expose the brass allowing it to oxidize(scientists don't crucify me if I used the wrong term for the metal type). Silver is more durable, but as a general rule, use luke warm water in the bath tub when washing with a little bit of dish soap(for cleaning purposes as well as softening hard water depending on your source, some areas have harder water than others and may require a little more soap). I put a unimportant towel at the bottom of the tub to protect the finish from being scratched by the tub or any dirt loosened during the cleaning process. Let the horn soak in the water for a few hours to soften any material inside the horn, and then clean the tubing with a snake brush. Any major cleaning can be done at a shop, but some are better than others... as you may already know. Dry the horn with a towel and then oil valves and grease slides again.
Playing: encourage your children to rinse their mouth out with water before playing to help keep salts and sugars out of the horn as much as possible as they can corrode the metal on the inside of the horn. Foods can also gum up valves and make them slow.
Storage: do not leave in excessively cold areas as this may cause the valves to seize up. excessive heat may cause the grease to liquefy and move into the valves as well as making the slides dry and hard to move.
And I think that't it...... haha I know it may seem like a lot but I just wanted to make sure I covered everything, because I didn't know things a brass player should have know for a while so never hurts to cover everything.
Again please feel free to ask more questions or ask for pictures.
Adams E1 SS, Gold Brass Body .6mm DE Euph N103 Jcup, J9 shank
Meinl Weston 2141 Eb Tuba PT 84