You "love Katahdin" but don't know which trails to take? Would this be one of those long-distance love affairs?
That and "intermediate level" - what does that mean?
Start with a basic trail map - the MyTopoMap link on the Katahdin page on SP will do, or get a paper one (suggestions can be found on the park website). Then go to your favorite weather service and check the average weather for the nearest town (millinocket) in October - that'll give you some idea (subtract a bit of temperature and add a bit of wind for summit conditions).
All the trails are pretty steep and all of them have the same elevation gain, the main question is whether you're afraid of heights - if so, avoid the "knife edge" route.
Most trails described on the Katahdin
page here on SP. Come to think of it, that page has a link to weather conditions too.
PS READ THE PARK WEBSITE. There are lots of rules to be aware of.