Some of these are a must but some are just things I find nice to have, they help me with projects :)
Some where safe to store your work out of the elements I use plastic boxes as bags aren't necessarily waterproof and can get squashed :)
Every kit you buy will have a needle and you may just build up a collection that way but if you want to kick start your stash they are cheap and easy to find in craft stores local or online.
Make sure they are sharp! You want a nice clean snip it makes threading needles much much easier. I use thread snippers they were cheap, work very well and have a cover over the blades so no accidential damage to your project while in the box being transported somewhere.
This, as I've said before these are optional and depend on the stitcher. My advice is to be willing to try with a hoop, without a hoop and even then all different kinds of hoops and frames :) If you have cross stitching friends they may have hoops you can try for free.
Cardboard Floss Bobbins
These are very optional, I like to have them to keep me from tangling all my threads up and having written on each bobbins the colour number and symbol, the brand and the brands colour number. This helps with more difficult designs that have only one tiny difference between two colours! By cardboard bobbins I mean I cut up tissue boxes and similar things to the right size, cheap and recycable, easy to write on :)
Thread brand conversion charts
They may come in handy if you think your missing a colour or run out of it, it may be that you have the shade just in another brand! I downloaded the charts free from the internet, for free how can you go wrong!