Hey Daniel, I don't think you will be able to rent a motox bike but if you could it would be expensive so save that money towards your own bike.
Your own bike, as a beginner, would be better being on older model for several reasons. An older bike is cheaper to buy, you can learn to maintain it yourself and when you take a tumble you will only add to the scratches of time and racing (battle scars) so you won't freak out. But a bike that was very popular in its 'hay day' like a Honda XR80 or XR100.
Then you need some basic riding gear for yourself, look around for 2nd hand for most of it. younger people grow out of their gear and it could be like new. Don't think 2nd hand for a helmet, buy a new SNELL approved helmet for racing, look for the tag inside the helmet, if it isn't there then it isn't a racing helmet so you won't be allowed to wear it on a race track, even for practice.
Find out where your nearest race track is and when the practice days are as well as race days. Ask Mom or Dad to take you along for a practice day and you should be able to get into the pits. If you see guys sitting about don't be too shy to ask them questions about how they started and advice for you, if you see someone working on their bike ask if you might be able to help in some way, even just holding something or passing tools, be friendly and helpful but don't ask questions till the job is done. If you find someone local then ask if you can learn from them. Most guys will offer you some sort of help if you ask, especially the 'older guys' who want the sport to grow.
You will need money and the support of your parents. Find some local job where you can earn some cash and bank it towards your own bike. At 10 years of age I cleaned up behind cows in a milking dairy for my start, it wasn't rocket science but it was cash. Mow peoples lawns and get a regular clientele and do the very best job you can do at whatever it is.
Best of luck to you, keep a good attitude and come back to the site as you go along and need some advise....