Mad Man -
I'm 48 now, but started in RC when I was your age. You can do this, and if you do, I PROMISE you it will help you a lot later. The hobby led me to become an electrical engineer, and taught me more than most of the courses I took in college. I agree with the recommendation to find a club - most folks at flying fields will fall all over themselves to help you, once they decide you are serious about it. Also, see if your local hobby store has a guy that will help.
No, you do not have to understand electronics ... yet.
There are many types of RC planes ... electric (big), electric (really small), gasoline powered (really big), alcohol powered ("glow" in the hobby, range in size from 24" to >100" wingspans), sailplanes, float planes, racers, scale models, sport models, acrobatic, really crazy acrobatic ... there is not enough time in your lifespan to experience every facet of the hobby.
There are several magazines that always have beginner articles ... look at RC Modeler, Model Aviation and/or Model Airplane News.
One other thing. You are on a tight budget. You have the luxury, believe it or not, of spare time that most of us in the hobby do not have. You can trade off that spare time for a cheaper alternative - buy someone's used stuff. There are always swap meets, ads on sites like this one and someone locally selling something. The problem is ... it might have problems. That is where the spare time comes in!! If you go this route, be ABSOLUTELY sure you take an experienced person with you so you do not get conned into buying garbage - there is a lot of that out there. Good Luck, and if I can help with info, mail me!!