If you aren't bottling, don't bother with a bucket with a spigot, your siphon will work better for moving beer around from your different vessels. If it isn't an auto-siphon, I would recommend getting an auto-siphon but it isn't necessary. I am assuming when you say "brewers bucket" that it is set up to be a primary fermenter (holds at least 6 gallons, has a sealing lid that is drilled for an airlock)? If not and you plan on doing the standard 5 gallon batch then you'll need a bigger carboy/fermenter as you need usually need at least 1 gallons worth of headspace in the fermenter after you add the beer.
Outside of the normal stuff included in a starter kit, my next homebrew purchase would be a pot large enough to do full volume boils (about an 8 gallon pot for 5 gallon batches). But it isn't necessary to start, you can do partial boils with a smaller pot and still make good beer.