Other than regular equipment for sewing (scissors, seam ripper, a really good needle threader, pins and needles, etc.) there are only a few essential things to get you going.
---A good rotary cutter and mat - Get the big mat because you'll regret getting a smaller one once you get started. With the big mat you can cut across a folded width of fabric (22") and still see the markings. The smaller ones will hide the lines and you won't be accurate. I like the 60mm cutter. It's smoother and seems to last longer than the 45mm one.
---2 rulers with those dots on the bottom that resist slipping - You'll need a long one to cut across the folded width of fabric (22"). I like my 5 x 36 one really well. And, you'll need a square one for squaring off corners of your quilt or cutting angles. I like the 12 1/2" one the best. Larger ones are SO BIG, and smaller ones don't let me cut my corner far enough for my liking. Get one that has marks along the 1/4", 1/2", 3/4" lines, not just the 1" lines. It should have diagonal lines for 45 degrees, 30 and 60 degree lines are a plus at times.
Now, there are lots of other things that make quilting easier or just a lot of fun.... and I have many of them, but those basic items will get you going and you can add more things as you need them and can afford them. Getting good equipment is a little costly but you'll save yourself time and trouble and won't need to replace it all quite as fast.
Good luck with your quilting..... find a good class to get you started or a friend that has been bitten by the quilting bug and you're off to a great passion, just like the rest of us.
nanna