First of all: prepare yourself to have an incredible year ahead of you. I loved my year in the US - it was definitely a life-changing experience.
I guess the state you should go to depends on your definition of "good". Do you want to cheer at a "big name" gym? Or do you not care about the name but about the coaching and reputation of the gym? There are many factors at play for choosing a gym to cheer at. One of them is definitely finances. Depending on the choice of gym, the financial commitment could be very different. Questions to ask would be: what is included in monthly tuition? Am I expected to take privates? Are the uniform and practice wear included? How much travel will be done? I know there were some threads "back in the day" here on the boards that had a lot of good questions you should ask before choosing a gym.
One important thing to consider: if you do Allstar you need a host family that would be willing to support you. You would need someone to drive you to practice (and there could be a lot of practices around Nationals season and/or Summit/Worlds) and to competitions. My guess is that you either need a host family that lives very close to your gym or that you need a host family that already has a kid in cheer.
One possibility to get a "lighter" commitment would be to do Allstar prep. The teams usually start in the fall and therefore require less money and time commitment. Therefore you could get the Allstar experience without the Summit/Worlds team price tag. An advantage would be that you would already be in the US for tryouts and wouldn't need to coordinate everything from Sweden. You'd also be there throughout the whole season while you'd miss out on quite a bit of practice with a full-year team.
In general, you should be able to do Allstar cheer as an exchange student as long as you can pay the bills though. I mean it is a business after all and any owner would love to have additional customers.
For high school cheer: that is highly dependable on your high school and the coach. Even though I didn't cheer back then I wouldn't have been able to cheer for any fall sports at my school, because tryouts were right before summer break and unless they desperately needed someone else, my coach would not have taken someone missing all of the summer practices.
There were later tryouts for competition cheer and some other cheer teams (maybe basketball?) which I could have tried out for.
An advantage of doing high school cheer would be that someone from your host family would only need to drive you to the school, or someone else from your cheer team could probably also pick you up at home. The cost would also be a lot less than Allstar cheer.
In some states, you cannot do Allstar and high school cheer at the same time, while it is no problem in other states. Depending on the state there are also very different rules about competition cheer - some cannot travel outside of their state while other high school teams can travel very far for Nationals.
All of the advice above is highly dependent on your location though and is just general information.
