There is a big spread between what is the overall best equipment for acquiring these types of images and what is the best equipment to meet this individual's particular needs. Full frame sensors of the same generation/technology and with roughly equal pixel counts will have a noise advantage over a crop sensor given their relative pixel size and light gathering capability but a current generation good crop size sensor will easily outperform an earlier full frame in the noise department. I use primarily full frame now but I still have and use my old 1D Mark 2 with its 1.3X sensor and I loved that sensor size for outdoor sports but it doesn't provide the high ISO performance I need for night or indoor games.
I do some band and cheerleader shots but primarily soccer and football players where the shutter speed has to remain very high for the fast action. For what I primarily shoot, at night F2.8 is the "slowest" lens I can reasonably use because in addition to the shutter speed/ISO trade-off I also need the fastest/best AF performance which also comes from using a fast lens. For shooting the band the requirements are a little less demanding given the somewhat reduced action speed and a 70-200 F4 would do although I would still go for the better F2.8 version if the budget permits and this lens will serve you well into the future. For my usage I would take a used older non IS F2.8 over a new F4 with IS but that is because of my primary focus upon action sports. The 70-200 F2.8 is a very good and very versatile lens and tomorrow night I will be using a 300 F2.8 on the 1DX 2 with the 70-200 F2.8 on the 1DX which is a pretty good Friday night football combo. For indoor soccer I am going to experiment with trying the excellent and relatively inexpensive 135 F2 on the second body to see how that works compared to the more versatile zoom. For what you are shooting, a good current crop sensor body will work fine BUT keep in mind shooting requirements in the future so that whatever you buy now will also suffice for anything you will be doing in the next few years. In my overall budget if I was dropping back a level on something I would drop back on the body before dropping to a less desirable lens.
You want to be as close as possible to what you are shooting in order to take advantage of as much available light as possible and given the often poor and varied field lighting of most public school facilities you need to plan your shots in advance to get the student shots you want when they are in an optimal location. With the band you can find out the program in advance and be prepared for what they are going to do at each point during the on field part of their performance. You might even attend a practice session (if permitted) so that you can make notes of shots you want to get during the actual show and to figure out your desired placement. If you want really good photos of the band on the field, at the very least get as far forward in the stands as you can while still maintaining a clear view but if where you are shooting is like most public schools there is a track surrounding the field and you can probably get access to it. Talk to the school AD or other admin about sharing photos with the band director, yearbook staff, etc. well before the event and this should help you to gain field access. At the high school level this is usually a pretty simple process especially if done in advance and this "diplomatic immunity" will usually work when visiting other fields once you know the band director. When playing at other schools I will go in with the coaching staff, AD, or trainer in order to ensure field access; the exception was when we played at a university facility and then I just went through the typical media access process. If the images you take are of benefit to the school then the relevant administrators will be your ally in helping you to acquire better images AND they will be familiar with the school policies on image usage so that you don't inadvertently provide images to the wrong people. I wouldn't send a group of images directly to a booster club or other "unofficial" school affiliate without a full understanding of the school policies. Don't do anything that will damage your field access opportunities.
Make sure that you stay aware of your surroundings and stay in the clear. At many high school fields timing is pretty tight for halftime and you don't want to be between the football players and the field entrance when they get ready to go back on near the end of halftime. One of the funnier scenes I have witnessed in high school football was a rather out of shape photo guy struggling to run at the head of the players entering the field; he wasn't trying to get photos of them but had been shooting the band and didn't realize he was in their way. It looked like a bad U.S version of the running of the bulls.
Some of the players got a laugh out of my fast footwork at the last football game I shot because an opposing player was determined to make the catch even though he was about 10 yards out of bounds and I did a very fast reverse to clear the area. I was invited to attend the next team practice in order to demonstrate my fast reverse. This is a reminder that YOU are also being viewed while doing photography so don't trip over the players bench or accidentally tackle an official while capturing images causing embarrassment to YOUR student. At that game my daughter and several of her fellow soccer players motioned me over to the stands to exchange high fives in recognition of my not getting tackled; I have coached most of them over the years and my daughter has a great sense of humor 🙂
Most importantly, resolve to get the most out of whatever equipment you are using so that the gear can fully deliver all that it can provide. Technology is a tool that is too often used as a crutch; whatever new gear you buy will provide better results compared to your SL1 but make sure that you also take the time to upgrade your technique as necessary and newer gear will open up new possibilities so prepare to do some new and different things with it rather than just focusing upon areas where it has improved over your current body and lens.