You asked a lot of good, but tough questions...
Unfortunately it's not possible to tell exactly what engine it is by the block casting number. Like Scotia said, you need to check the bore & stroke and even that isn't a guarantee since someone in the past may have overbored the block and changed the crank. A C6ME-A could easily be a 352, 390, 410 or 428. If it has a "scratch" mark on the back of the block in the bell-housing area like "A" it could be a 428 and that's like hitting the lottery! Many 352 and 390's came with 2bbl carbs, both cars and trucks so that doesn't rule them out. The carb should have a tag attached or I.D number stamped in the base of the carb near the drivers side front. If you post the number we may be able to I.D. the carb. But as far as getting basic parts from the auto parts store most things will interchange between the various FE's. Knowing the model year can help for some things like sensors, etc., so as was advised look for a date code under the oil filter adapter.
As far as pulleys, there are literally thousands of possibilities and you'll have to play engineer a bit to figure out what you'll need. I'll say right up front I think the easiest and cheapest thing would be to get a whole set from a '70's pickup truck FE. That would also include the harmonic balancer and pointer and the alternator brackets. Do you have salvage yards nearby with older cars and trucks? You may want to advertise here and on the other FE forum. Buying a cheap 360/390 off Craigslist and raiding the parts you need is another possibility.
This is tough because there were a lot of changes over the years. Older vehicles were less likely to have power steering and A/C so it's harder to find original multi-groove pulleys. They became more common as we entered the '70's. Many pulleys had multiple uses and if one of those uses was on a muscle car like a 428 CJ or 427 SOHC the value of the pulley skyrockets. Many pulleys will interchange between different engine families, more so with the waterpump pulleys. You can look at 240 6cyl. and S.B. Ford waterpump pulleys also. 429/460 waterpump pulleys use a larger centering hole. Ford made a change in the bolt pattern of the FE crank pulley in 1968 I believe, slightly wider spacing. That's why I suggested above if you go with a '70's truck set-up to get the balancer and pointer also. And know that the balancers and pointers often times go together, so double check whatever you have ( even the current set-up ) that zero on the balancer is actually TDC. Many pulleys had an I.D. number stamped in them, but some had a ink stamp, now long gone, or no I.D. at all. If it has an I.D we may be able to look it up in the Ford parts book, but again, not all I.D.'s are listed. And then you also need to check the size fit. There are large diameter waterpump pulleys that will not clear a large crank pulley. You will also need to check that everything lines up for the belts, although some of that can be solved with spacers behind the waterpump pulley or changing the alternator spacer, etc. And finally know that the Ford engineers spent a lot of effort matching the size of the pulleys to the speed they wanted to turn the accessory ( like waterpump, alternator etc. ) I wouldn't worry too much about it just to get the car running, but later you may want to refine what you have. I hope this doesn't scare you off, it's all solvable, but not as easy as it was years ago when salvage yards were full of these cars. Don't be afraid to keep asking questions, we'll try the best we can to answer. Also let us know where you live, a fellow forum member may live nearby with what you need.