Anything that holds water will work. I use a cheapo 10g with a strip light, a hang-on-back filter, and a heater. You could just as easily use a rubbermaid tub.
It's preferred to use a cycled tank, but in a pinch you can set up a hang-on-back filter on your main tank for a week and transfer that filter over to your quarantine. That way, you'll have at least *some* biological filtration on the new tank. You'll probably see ammonia for a bit, but not like a totally uncycled tank. Just keep testing for ammonia and nitrites and do daily water changes as required.
Ich will survive as long as there are fish around. So if you have more than just the clown in your main tank, just treating the clown will not necessarily rid your tank of ich. Safest course of action is to put ALL fish into a hospital tank, treat ALL the fish, and then leave the main tank fishless for 6-8 weeks. Without fish, the ich will die off in that 6-8 week time period and your main tank will be rid of the little buggers.