Some basics in quilting are different from the basics in sewing - clothing, etc. What do you want to concentrate on? This board is almost completely about quilting. If you are going to be regular sewing, and not as much quilting, you might check out the site SewMamaSew.com The are primarily about sewing and less about quilting.
For anything, you need:
a good pair of fabric scissors - it's not worth it to skimp in this area and there are many brands out there - use coupons to get the best you can purchase..and keep them ONLY for fabric!). .....
A pair of paper/non-fabric scissors (cheapies will work, just replace them as soon as they are dull)....
Good pins are essential in both quilting and sewing, but there are different kind of pins as well - I'd suggest a pin with a glass head (so they don't melt if you touch it with an iron) and about one and onequarter inch long......
A good pincushion,.....
seam ripper (we've all been there!), ....
tape measure and I've always liked to have a good 6 inch ruler handy for measuring.....
machine needles. replace them every 8 hours or so of sewing to ensure the best result (personally, I don't do it that often, but I can tell when the needle is dull, and dull needles do make a difference....
hand sewing needles...you'll need a few of these, but type depends on what you are doing and what you're comfortable with.
For quilting there is an additional list of things and lots more sewing notions depending on what you plan to sew. Others will add to this list, I'm sure.