What are certain basic stick types used for(musical situations)?
like.... 5A, 5B, 7A, 2A, etc.
There are no hard, fast rules. So much depends on the physical attributes of the player, their touch, and their training - i.e. what they're used to. A couple of examples: Steve Gadd does everything with relatively small sticks, while Vinny Colaiuta does everything with sticks close to a 5B in size. A key ingredient in their stick choices is the size of their hands.
That said, you will find that jazz players will tend to use lighter sticks - 5A or smaller, while players playing heavier music will use heavier sticks - i.e. 5A and up. It's hard - though not impossible - to play light swing with parade sticks. It's equally hard to play super high-volume live rock gigs with Vic Firth SD5 Echos.
The only way to really find out what works for *you* is to try different sticks in different situations and see what is comfortable and makes your desired sound and style easier to obtain. It can be an expensive process, but trial and error is the only surefire way to figure out what feels comfortable in your hand and has the qualities you want. I have a box full of dozens of perfectly good - but hardly used - sticks in every size, shape and colour to attest to my own search. I'm sure there are others around here who can relate.
