It depends on the fish. Quarantine should always be heated (depends on the fish), filtered & cycled. IMO quarantine should be only a little smaller than the main tank, 'cause you'll want to keep them in there for around ten weeks.
The longer they in, the less likely they are going to transfer disease. While I do agree that 10 weeks is a little excessive, I'd aI'm for a month personally.Where dovyou get 10 weeks from. 2 weeks is usually long to diagnose and treat any problems if there is any.
As fot size 10 to 15 gallon is enough, most fish will be fine in a smaller tank as long as you keep the water clean and its cycled.