#1 I'd recommend an 8 gal bucket. Super easy to use, blowouts-not a problem. For carboys, I like Better Bottles and have a couple.
#2 Not very important at all to start. Down the road add a carboy to secondary things like fruit beers, to dry hop (you can also just do it in primary), or to bulk age high gravity beers for a month or 3. I also use my 5 gal Better Bottle to primary ferment 2.5 gallon batches of higher gravity or experimental batches.
I only have 1x 8 gal bucket, 1x 5 gal BB and a 3 gal BB to bulk secondary age high gravity 2.5 gal. batches. My next addition will be another 8 gal bucket so I can have 2x 5 gal batches in primary at once.
As far as clarity, I don't do anything...no additives, rarely cold crash, no secondary. Just about any beer will be crystal clear after a few weeks in the fridge...until then, hazy beer taste the same! Ironically, the one beer I wanted to be clear (I cold crashed and secondary aged it) was my Golden Strong ale...it looks like murky pond water after many weeks in the fridge and I don't know why, oh well.