holley or edelbrock 4BBL carbs are both very simple designs and either would be a really good choice to do your first rebuild on
basically, all it consists of is dismantling (for an edelbrock or holley, you basically just remove the top plate), cleaning, get 3 or 4 cans of any brand carb cleaner and spray all the little holes everywhere, almost all of them go somewhere, so when you spray in, you should see it come out somewhere, and replacing the rebuild parts as you reassemble it (mostly the needle valve, the primer pump in some kits, and a ton of gaskets).
First of all, you'll wind up with a lot of little parts, and they all hafta go back in (rebuild a tranny and it's ok to have a couple screws left over in most cases, but not with a carb. extra parts are very bad). So you want a clean workspace with some real estate. I have an old cookie sheet I swiped from my wife that I use for stuff like carbs where I need to keep track of parts and one of those little magnetic trays. They also all need to go back in the same place they came out. most rebuild kits have an exploded view diagram, and you can always find one on google to print also. keep it straight in your head (dismantling one weekend and then leaving reassembly for the net weekend is a bad idea), take pictures as you go, write notes, whatever you hafta do to keep it straight
for an edelbrock or holley, it shouldn't be a huge issue (first rebuild I did was a mitsubishi-built dodge 2BBL... jets everywhere, two priming pumps, linkage for days going every which way... it was rough).
make absolutely certain you don't score it anywhere. use solvent and a toothbrush (no wire brushes) to remove old gaskets, no scrapers... they are very sensitive to even the slightest air leak. better to leave some built up crud left on it than to scrape a score somewhere that will let air leak.
pay particular attention to the jets (brass rods, about 2-3" long, tapered on the ends), you want those as clean as you can get them, but no abrasives, and you want the little holes they go into as clean as you can get them too. They basically control the amount of fuel that goes into the venturies (the two little round deals in the pic, vacuum from the engine sucks fuel out of those in a small enough trickle for it to vaporize).
also pay attention to the needle valve (small brass torpedo looking thing, about 1/2" long with a rubber tip) and the brass ferrule it sits in. a good kit will come with both the seat and the valve, but you can usually get away with replacing the valve only as long as the seat is clean (they usually stay very clean unless you have bad gas in your area) if you remove the seat to clean or replace it, make absolutely certain that it is seated well. a leak at the bottom and the valve won't work.
*** the needle valve shuts off incoming fuel at a certain level, if it (or the float) fails or leaks, the bowl can fill higher than the level of the venturies and fuel will leak out of them, that sounds like what's happening to your carb. ***
lastly, the float. first, make certain it floats
just drop it in a cupful of gasoline. when you put it back in, you'll need to measure the float level. how you measure and adjust that depends heavily on the carb, so you'll hafta google it (if it's a holley, it will have a set screw and a little scribe line IIRC, super easy). In any case, it's a critical adjustment, and in most carbs it's really the only "tricky" part of the whole deal. 90% of the time, you don't replace it and there's no adjustment needed.
*** if your float sinks, it will hold the needle valve open. this can also cause the dripping fuel problem you're seeing***
It sounds a lot more complicated than it really is. As long as you keep track of where everything goes and get the float where it's supposed to go, it's basically just a thorough cleaning