The local county shop here starts most of their guys off in the install bay. The last two guys they hired were actually mechanics from the auto repair industry. They had some electrical/electronic background.
After a few years of crawling around in police car trunks installing radios, lights, etc, they eventually got bumped up to bench techs.
On the job training, manufacturer classes and real world experience has made them into good techs.
It seems that gone are the days of techs doing component level repairs. With the newer equipment being surface mount technology, it's getting unrealistic for smaller shops to do that sort of repair. More often board level swaps, or just sending the whole thing back to the repair depot is what happens.
I'd strongly second the network training. The latest system I am installing all connects via IP. Understanding network topology, VPN's, etc are all involved. Newer radio dispatch consoles are starting to be voice over IP, too.
Tower work can be pretty specialized, and not all techs in this area are expected to do that. Usually employers require specialized training (com train, NATE, etc.) If you are not OK with heights, I wouldn't worry to much about that. Of all the guys I know in the industry, only two of them climb towers. More often than not, they will contract that work out to specialists.
A good, well rounded background in many fields can serve you well. Most good techs that have been around for a while have a good mix of experiences. Some things that can be helpful:
Telephone/Telecom
Mobile Installation
Electrical
Electronics
Automotive technology
NETWORK!
basic mechanical skills (being able to do some basic fabrication can be a plus).
Another good place to get some experience would be by getting your amateur radio license. While it, on it's own, won't get you a job, it will get you some very basic understanding of radio systems. Often a radio tech that has been around for a while will often be a ham. Being in this line of work usually requires a lot of late hours, hard work and not necessarily the best pay. You gotta love what you do. Guys that love radio will often enjoy it as a hobby as well as a vocation. I know many commercial radio techs that are hams on the side.
You are young, so don't overlook the military as an option. 4 years of commitment will get you a world of experience and training. Don't overlook the US Coast Guard as an option, if you aren't into the whole combat thing. I did a couple of years there when I was about your age, and it was by far the best decision I ever made. No (and I mean NONE!) other option will compare to what you get out of it.
If that isn't an interest, check into the local community colleges, they can be a great inexpensive resource. Most will over some networking classes, and often they will be night classes so you can keep working during the day.
Good luck to you!