I have the Bach Tr600 a intermediate trumpet. I started out on this trumpet and still play it 4 years later. Bach is a really good brand to buy for begginers. I bought mine used from my local music store. I would stay away from buying online.
The mouthpiece is 5c. 7c is for smaller lips 5c slightly bigger and 3c for bigger lips and more room.

Step 1: The Parts

Having all the parts to a trumpet is important.
In the first picture there is the 3rd valve slide. This is important when you get really good. There is also the ring finger holder. That is where you put your left hand ring finger.
Second picture is the 1st valve slide, also important when you get better. There is also the thumb saddle where you put your right hand thumb.
The third picture is the pinky holder and your valves. The pinky holder is where you put your right hand pinky. Your valves are numbered 1 2 3. 1 is the valve closest to you when playing. followed by the second and third.
The fourth picture is your tuning slide and water key. Push your tuning slide in to make it sharp and pull out to make it flat. Trumpets usually tune to C. The water key is where your spit is emptied. Just press it and blow it out, don't buzz it out.
The fifth picture is your other waterkey. Do the same thing by blowing it out but also press down your third valve button to get all the spit out.

Step 2: Cleaning and Repair

valve oil goes into your valves of course. Put your valve oil in the bottom of your valves. There are holes there. Also on your valve slides you put the oil.
Tuning slide grease helps your tuning slide move smoothly. If your in a school band conductors hate when tuning slides don't move.
The pipe cleaner is used when you give your trumpet a bath. You do this about twice a year. Take all valves and slides out and put it inside a bath tub with cold water. Take you pipe cleaner and clean out your valves pipes and anywhere it can go inside your trumpet. I was told to never use soap.
I personally don't have a mouthpiece brush. I boil hot water and put my mouth piece in. It gets the job done.

Step 3: Playing

When playing you must have tight lip corners. loosen them when playing lower notes and tighten them when playing higher notes. Faster air movement is better for high notes. For first time practice, just buzz on your mouthpiece going up and down like a siren.
Good posture and breathing technique helps produce a better sound. Breathing in and storing air in your stomach gives a lot of support. Don't breath in to your chest.