"Together, we are more than the sum of our parts." That's the essence of what team building is all about. We can work well as individuals, but do we integrate well?
Here's what the most successful teams do:
know what everyone does, in detail.
know each other's strengths - and what they are less good at.
know what their objectives are (and remember, "if you've got more than 3 priorities, you haven't got any." Jim Collins)
have a supportive working environment.
have a culture of "finding a better way" to do things.
believe in learning - including learning from mistakes.
integrate new members quickly.
When thinking of team typologies, the work of Dr Meredith Belbin often springs to mind. A psychometric report into each person's preferences could be a good starting point.
More accessibly, Pack Types allows people to decide for themselves, are they a terrier, a sheepdog, a retriever, a guard dog...? Great fun and very illuminating!
Most importantly though: this is not a "one size fits all" deal. We'll need to know what your needs are - then we can think about what your team build could look like.