The Cranks tend to come with the spindle when you buy the crankset. Some come with tools; others don't. Like Mike G said, some won't need a puller. Wait til you choose a specific crank and ask again.
The front sprockets for most cranks, as well as the 3-tab rear sprockets for modern coaster hubs, come in both the 3/32" and the slightly fatter 1/8" varieties. You can run 1/8" chain on either size sprockets, but you can't run 3/32" chain on the 1/8" sprockets. Shimano offers 3/32" sprockets with their trim kit, and all the current-production Shimano 3-tab sprockets are 3/32". Sturmey-Archer makes compatible units, and offers them in black or chrome, 3/32" or 1/8" pitch.
(Just get the Sturmey-Archer sprocket for 3/5 speeds. The 8speed ones are huge and won't work; the splined ones for the S3X are just hyperglide-pattern, and won't work, either.)
(Mike G, FYI, the Nexus uses the same types of sprockets as the CB-e110, but they sell nicely-finished Nexus "cogs" and crudely-finished CB "cogs"... you can run either, or either hub. I tend to run the Sturmey-Archer sprockets, as they come in a wider pitch.)
Basically, you can run 3/32" OR 1/8" chain if both front and rear sprockets are 3/32", but if either or both of the sprockets are 1/8", you'll have to run the wider chain....
Worksman and some mid-school bmx bikes run even wider 3/16" chain. It looks cool, but ease/cost of replacement has led me to avoid it in favor of 1/8" chain. My favorite is the extra old-school KMC 410H, which runs bushings! (interestingly enough, KMC makes a nearly identical chain, the 415h, in 3/16" size...)
HTH
-Rob
PS- there's a lot going on with crank/frame/rear end compatibility. Hopefully, this gave you an idea of what to look for and how to plan, but you might want to ask on here about the specific components you're looking out, before you actually buy anything. For me, if I buy just one incompatible part, it'll drive me to fits of frustration, and then I'll end up building an entire bike around that part. So, it pays to ask before you buy....