Hey I am looking to get into 3-Gun competitions... I am 17, living in Madison, WI , and very interested. Where should I take training courses, where can I spectate shoots, and where should I buy the guns for competition? Also; any suggestions on how to become a firearms engineer?

I live just a bit north of you in Portage.

I would hold off on special training for now and jump into watching/shooting matches.  You could start this sunday at Winnequah Gun Club with their last 3 gun match for the year.  They are just a few miles north between Lodi and Poynette.

http://www.wingunclub.org
http://www.wingunclub.org/changing%20Docs/2013-Outdoor-Calendar.htm#Sep

I would recommend that you also shoot USPSA matches if you are not already doing that.  Winnequah has monthly USPSA matches throughout the entire year (indoor during the winter).  They also have a weekly USPSA League that is a great way to get some shooting in every week.

Additionally, you might want to look at doing an Appleseed for some rifle training.  If you have a .22 rifle and a sling, you are ready to go.
http://www.appleseedinfo.org/  

If you get rolling now, you should have enough matches under your belt to attend one of the 3 gun junior camps next year.

If you need any other info or advice, feel free to email me.