clematis
Doug says: In order for this plant to go dormant, you have to reduce light levels (naturally going to happen) and you have to get it colder. So it will naturally go dormant outside.
The trick is in keeping it in the high 30's to very low 40's (no higher) to keep it dormant without freezing the roots solid. If you have a cold cellar, you can do this there. No cold cellar, no overwintering.
If the plant doesn't go dormant, it will live for quite some time in the house but the second year outdoors, I'd bet on it fading away or being a little tricky to keep alive. They want to be dormant for that 8-12 weeks or so.
What size pot? Probably something in the 16-inch range would do nicely for long term success without adding heat stress on the soil. Remember that this plant wants a cool soil if it is to grow properly so smaller pots will heat up too much in the sunshine.
Good luck with it.