Viper,
The cut leaves don't mean anything. Some get trimmed to fit into their packaging, that's all.
Potting soil is largely inconsequential. Anything that retains moisture but doesn't sit soggy for days should be fine. I used some cheap stuff from Home Depot for my latest batch of tissue cultured plants, and they're all doing great.
For pot size, you won't want to use anything larger than, say, a 2.3 liter pot (medium sized black pot used for 2 to 6 dollar plants in most nurseries) until the roots start filling up. Too large a pot means a lot of wasted water and nutrients. A smaller (yet roomy) pot means you can more accurately focus your efforts on feeding it, and the soil should warm up/remain warmer longer.
Though your Chicago summers should provide a lot of opportunity for growth, you're going to have (at least) a few months of slow-going. A 6" plant likely came from a tissue culture seller, like Wellspring Gardens, Florida Hill Nursery, etc. There's nothing wrong with that, but contrary to all the advertisements, tc banana plants don't generally leap up to 15' heights in a single summer.
Healthy pups that grow 8-10' in their first year usually start as healthy corm offshoots from a mother plant. They've got a lot of stored energy to work with, while tissue cultured bananas have only a few tender roots to get them going. Mind you, that doesn't mean you got a raw deal or anything, but it's like spending months learning to do something for yourself as opposed to having someone there to give you advice and tips to speed you along.
Spend the next two weeks letting it adapt to its new environment. Make sure it gets some sunlight, but don't put the pot out in direct sun until it adapts. After a week or two, start feeding it lightly with a low-dose of liquid soluble fertilizer regularly.
After the first month you can consider up-potting it and upping the fertilizer dose a bit.
March 13th, the day I received my Musa Black Thai
May 9th, almost 2 months later. Full sun, regular (light) fertilizing. Unpotted one of these the other day, roots fill less than 1/4 of the pot. Still plenty of room to grow.
