I make those Selection kits; you'll find them very easy. You need room in your bucket for a little more than 6 gallons. Sounds like you have the basic ale pail which is what I use - perfect size. I think the 6 gal mark is the 2nd ridge from the top.
The directions call for two rackings, so you need a couple of carboys. From what I understand, you need to be careful to have no headspace after the first racking. For that reason, I ended upo buying a couple of 6 gal carboys. You could probably use 6.5's, but you'll need to make up for the volume. I think Yooper suggested sanasized glass marbles.
You can let the kits sit. They're dry yeast so there is nothing that's going to go bad quickly.
Unlike beer, it's MUCH cheper to just buy the bottles. Buying full bottles of wine gets costly quick. You'll need about 30 bottles per 6 gal kit. So, either start asking people to save them or buy a few cases.
Hope this helps - I'm no expert. Also - making white or red? I might be able to suggest some good kits for you.
On Tap: Whatever I just brewed (got sick of updating it)