A short list of things that are handy. This is, very roughly, in order of importance to me. Things at the top of the list are nearly essential, things later aren't, but a lot depends on what you're doing and preference.
* Shears (I'd start with a set of 8" bent handle shears, I like these: http://www.wawak.com/products/product.cfm/pid/1279 )
* a 60" fiberglass tape measure
* seam rippers (there are different styles, try a few to see what works for you)
* an assortment of needles (sharps or microtex in 10,12,14 would be a good start)
* a metal or plastic rule 24 or 36" long (several, in different sizes, are handy. Wood isn't any good, it warps)
* things to mark on fabric with, both permanently and not. I use washable markers for many removable marks, and grease pencils for permanent marks
* an iron and something to use it on.
* a small sewing scissors
* thread snips
* painter's tape
* very sharp pins (I have exactly six pins in my pin cushion, and almost never use them. Many people seem to use them a lot, though.)
* a pin cushion
* a few hand sewing needles
* pattern paper (brown kraft paper is okay) for making patterns and templates
Things like thread, velcro, zippers, straps, hardware, etc can be bought to suit a planned project. If you do lots of work, it's worth buying extras of the things you use, so you have spares or can whip something up on the spur of the moment.
There are lots of others things can be useful (and I'm sure I missed something essential...), but you buy those as you need them.
Taking notes is a good idea. It's also useful to take pictures of things as you work on them, so you can remember what you did.