I'm a newbie to quilting, so I'll share the items I began with 3 years ago. I started with the Olipfa 6" X 24" lip edge ruler because it measures almost half the width of my fabric. I bought the Olipfa edge ruler so that it would grip the edge of my mat. I use it as my straight edge to cut straight lines. Within rulers, after the straight edge, make sure all the other rulers you buy are the same brand because they can differ in the ways they measure. I use Omnigrid the most and I prefer the ones that are clear with yellow and black lines. The second most often used ruler is my Omnigrid 4" X 8" ruler, which is used to actually measure my fabric into the straight edge where I cut.
Next, I needed a 45 mm Olfa rotary cutter along with the 18" X 24" mat. I like the green mat because I can see the fabric better next to a dark color.
Quilting straight pins that are longer are what I prefer to use. I bought the expensive smaller ones when I took quilting lessons because they were recommended, but I never use them. I find them difficult to hang onto because they are so small. I guess my hands are large and I got tired of picking the up from the floor all the time.
Thread is next. I use neutral colors almost exclusively, and I would recommend you buy good thread. I don't use Coats and Clarks ever. I've been using Gutermann when I could find it on sale for 50% off. I just received an order from Superior Threads because so many of my friends who quilt highly recommend their Masterpiece and/or Bottom Line for the bobbin. I buy white, cream and black most often. As I've branched out, I've added red, navy, emerald and a few pastels. You want the least amount of lint possible.
A good pair of scissors is next. I also used my Hancock's coupons to get a pair of Gingher Dressmaker's Shears for around $20; which was about half price. Make sure they are right-handed or left-handed whichever you are.
I use an inexpensive measuring tape when I need to measure the length or width of a project.
That's my recommendation for a basic beginner. As I have gotten more immersed in this, I have added different length and width rulers, a larger rotary cutter, different types of pins to use for various projects, Best Press Spray Starch, a pair of small thread snips that are spring loaded for beside my sewing machine. A smaller pair of Mundial scissors (about 6 inches long) for next to the sewing machine. A Bendable Bright Light and 2 of the "Ott" type lights to illuminate my sewing area; especially when sewing at night. A second small sized iron to keep at my sewing area instead of the one I use to iron clothes with. (although I NEVER iron clothes!!!) And I love my magnetic pin holder and my pin cushion, which I made.
And then, I got into the cutesy things like charms on my scissors, etc. which are totally a waste of money, but I love them and I don't care. I LIKE them!!!
You can go on ad nauseum adding fun and different things to your repertoire! It's always kind of fun finding a new notion or some way of making some task easier, more creative or more fun. Have fun and ENJOY it!