Unfortunately, starting and running a rescue involves a LOT more than just having a big heart and knowledge about horses. The best rescues are run either by rather wealthy individuals who can afford to foot the bills themselves OR are groups that have qualified for non-profit status. Being a non-profit has many advantages, such as the fact that people who donate to your rescue can receive a charitable contribution deduction on their income tax, and you also usually do not have to pay taxes on the supplies you buy. People tend to trust 501 c3 and similar charities because they know that the charity is using the money/supplies it receives for a certain purpose (in this case, to care for horses.) To be a charity, however, requires paperwork and a board of directors, and I'm not sure that you as a minor could do this.
Sadly, another BIG issue you would need to consider is insurance. Even our local non-profit rescue has to be careful when visitors come onto the property. If someone were to get hurt, the rescue could be sued. If a family adopted a horse and it bucked someone off, the rescue could get sued. Once again, this is why the most stable (LOL) rescues have boards of directors that include lawyers (as well as accountants, grant-writers, etc.)
I know that $1,000 sounds like a lot of money and you should be congratulated for saving it, but a rescue can go through that in one day or in one vet visit. Rescues require HUGE amounts of money. Many of the horses that come to them are in need of extensive retraining or must be on special feeding/medical programs. I don't know any rescue that gets all its farrier work and vet work free, even if it's at a reduced rate.
I know this is probably raining on your parade, but it's better to look at the situation squarely from the beginning than to start a "rescue" and then suddenly run out of money and then YOU have to find a rescue to take your horses. Many rescues end up "saddled" with un-adoptable horses- horses that are so wild, ill, old, or deformed that they will not find homes. These horses are on the rescue's feed/vet bill for the rest of their 20+ years of life. In a worst-case scenario, a rescue get a crazy horse that was drugged at the auction, and this horse becomes a liability for the staff and other horses.
Perhaps a better plan for you would be to try to find ONE quiet gentle old (but HEALTHY) horse or even a friendly colt that needs love and attention. Work with this horse, give it all your time and attention, find it a home and THEN get another horse to work with. Another idea is to work with a charitable rescue in your area for a while and get to know the business; then you can start your own rescue later in your life. If you could foster for a local rescue and train horses for them so that those horses might find families, then you could be doing a great thing for a good cause right now.