Hmm looks like a wide open field to explore, Nice question new climber!
So here are some general ideas based on what you said you were looking for that might help and that you might find you like--I offer them based on my own experiences and share some of what I've learned from others who know a lot more than I do because they've done more climbing sucessfully, more varied climbing and for far longer than I have and I second some of what everyone here has said on the thread with hoepfully some extra reasons why.
You mention you've done several top rope climbs which if it is true is not a lot. I would do a lot more to check that my experience covers the scope of different kinds of climbing moves I might want to use. For that books are fine to compare technical moves and strategies on moves and practice. And as someone said bouldering for balance and moves too.
Why do people fall in climbing? I guess it's a misstep, a loss of balance and then just simply that the climb step or sequence is beyond their technical ability. *** or see tradmanclimbz below for a good reason to fall. An inexperienced belayer could accidently pull you off , step off balance themselves at the belay, or worse not be there when you need it for some reason characteristic of human nature, like their mind wanders, they get confused, tired, make a mistake or become afraid. So you need to be sure you have good belay experience as a leader and as a second.
Falls I think happen way more often if you are changing your focus from the climbing itself to doing something else, like placing protection. So since climbing is more than just the feat of physically accomplishing the moves, maybe you could learn some interesting stuff by setting up the protection first from a top rope and getting used to leading your rope through pre-set protection on a route. Then using the same route you set up and practised from via top rope, you could practice placing the gear leading the route--- now that you have some knowledge of. Having some idea in advance allows you to be free to work on the coordination and balance aspects of the technique of placing protection securely--and helps get it down to more of a reflex than a slow struggle. Just an idea, which you may or may not find helpful. Some people are just naturals at balance.
Multi pitch climbs are really different from top roping and there is so much more to think about. And of course as others have said, you generally make more of a commitment. Maybe compromise, I agree with the idea someone mentioned of choosing established routes with fixed belays for safety and bailing out. Many in the guidebooks describe the kind of gear req'ts you might want to use so that helps--or ask someone in advance.
Also, you could practice with slings on less technical routes to develop some reflex thinking about how falls might occur, how might you protect yourself in a fall, and work a lot with your belayer on successful communication when you are out of view or sound and just plain get more experience belaying as leader and as second. I briefly checked out Ross Pond in the northeastern corner of Connecticut one time and there was some fun stuff to choose from there like this, Off route 395 I think.
There are generally lesser in nature and fewer in number objective risks, like falling rock, on estalished top rope routes although you always need to be aware of these possibilities. So making a beeline for rugged and / or remote terrain to begin playing and testing, placing your gear, when it will most certainly take you longer and you will be less efficient ,invites more risk.
A big part of climbing is learning to read the terrain. What you see from the ground looking up or down , what you see when watching other climbers , whether in leading you or from the ground on a sport route, never really, fully, reveals what it's like when you get there in fact climbing yourself. So again this takes a lot of experience and there are no short cuts in my view to doing the climbs first to learn how to do this, then leading someone else. Transitioning by doing both, with as someone said, developing your ability to read terrain by doing more climbing as a second on more technical climbs with an experienced leader to experience the variety of climb conditions and variety of terrain, then doing also your own climbs on less technical easier climbs leading is a solid strategy seems to me.
Shorter routes, short approaches can build more confidence for accomplisment in not getting stuck somewhere. If you don't have experience already then it's kind of hard to know how long it will take you to do the pitches on the climb. For me time flies really fast when climbing.
So in dealing with the many unknowns in climbing, having a full repertoire of ways to deal with a great variety of possibilities and even in good conditions, makes the best challenges more enjoyable and more successful. As I think everyone has said so far, experience in applying concepts, that is after you know them by heart, is the key to improving your climbing and safety while doing do.
For me, there is nothing like having someone who knows what they are doing show you. It's a much smoother process and ismore likely to build confidence which helps climbing and you progress faster. A hit and miss experimental strategy can work of course, it just depends on what you are looking for and what is possible for you moneywise. If you hire a professional or join with one or more to share the costs to learn from someone who is a good teacher and has solid experience, then even though you can't learn it all in one go, you will certainly have some parameters that allow you to successfully experiment more effectively on your own. If you have a lot of time, have many years to play around then it must be very satisfying to learn step by step on your own. Also why not try the many rock climb festivals around, I haven't been to it but somewhere on NECLimbs someone mentioned a Climbfest coming up around Boston. This is a great way I think to explore your options and talk to knowledgeable people in person.
People climbing at a cliff or wherever do kind of chat a lot, and people I find are very quick to offer up opinions on what you should do or not do just out of enthusiasm for the activity, HOWEVER, you have to take what they say with a grain of salt. That is, whatever they advise is based on their own experience, which can be very limited or very big.
I think everyone has a different comfort level with how they manage a climb and how they measure risk that they want to take.
In any case, best wishes for some great climbing---and lots of it!
(Just like the climbers at any cliff, it was fun sharing my long view with you . Hope it helps!
ps modification: I use a similar concept but in a different way like tramanclimbz says below. I agree that choosing a steeper climb to lead, pushing your limit I guess, and failing thus finding yourself hanging on a secure protection will be good experience because if it is all too easy for you on low end technical stuff, you don't reach the "desperate" move level where believe me you sure can learn a lot.
I"ve heard a lot about the idea of "pushing your limits" as indicated by a fall to hang sequence I guess, but it's not my thing.
I do really enjoy doing climbs which has a least one pitch way beyond my technical level when I second a perfect leader... the reason I don't mind falling in that scenario is that it is a controlled fall. I've seen a number of leader falls on highly technical terrain by other climbing teams, (not on my own climbs tho) and it is not I think so easy to control the fall that is accidental in nature. But also there are probably a lot of falls where you know you are about to go and just control the fall safely. So falling to is a kind of personal preference or choice often too.