These are the basic quilting supplies that I recommend and use myself for quilting.
Sewing Machine:
The great thing about quilting is it can be done on the most basic machine. I have upgraded my machine twice over the years for different special abilities but if your machine sews a straight stitch, you can quilt with it. Recently I purchased a travel machine for taking to quilt guild for $50 from Facebook Marketplace. The main thing I miss when using it is my automatic thread cutter and lights. You can get an LED light strip to mount to the throat of your machine which helps ease eye strain.
Rotary Cutter & Scissors:
A 45mm rotary cutter for cutting the fabric. I highly recommend an ergonomic version if you don't have one. I currently use the Fiskar's Adjustable Three-Position Rotary Cutter (45 mm). It is so light and the most comfortable cutting position for me. I use it with Olfa's Endurance titanium blade.
Quilting actually doesn't require a lot of scissor use - although they are handy to have for trimming threads and making cuts here and there.
Cutting Mat:
I prefer a larger cutting mat at 24" x 36" wide. Mostly because it gives me more room to lay the fabric flat and cut more strips before shifting and re-aligning. I like a double sided mat - some of them have different measurements on either side so watch for that. Self-healing mats will last longer. This Fiskars Mat is my current cutting mat.
Rulers:
My go-to rulers are 6" x 24" and 2.5" x 12". Both of mine are non-slip and I recommend clear with black lines. I use those two rulers ALL of the time. To make Half-Square Triangle blocks (a very common block) easier I also recommend a 6.5" square ruler with 45 degree angles marked on them.
Pressing:
I can not stress enough how important pressing is through the whole quilting process. Pressing makes a world of difference when it comes to fitting pieces together and having a well squared quilt. I currently use a Chi Iron from Costco - the higher Watt means it heats faster. It also has great steam functions.
These are not essential but I highly recommend them: a Wool Pressing Mat and a Tailors Clapper. Both help significantly in getting a beautifully flat seam. I prefer to press all my seams open because I like that look - but no matter which direction you press they make a difference.
Thread:
100% cotton thread is recommend for quilt piecing and quilting. Too strong of a thread can actually cause wear on the seams. My go-to brands are Aurifil and Guterman for piecing. I frequently use So-Fine and Glide threads for the quilting.
Batting:
My go-to batting is an 80/20 cotton poly blend. I like both Quilter's Dream and Hobbs. The choice for batting affects the weight, feel and look of the quilt. Cotton blends usually result in a flatter appearance, Polyester has more loft. Wool is really good for cooler climates and so on. You can ask to see and feel the batting options at a local quilt shop or from a friend who might even be able to cut you some samples.
Fabric:
I prefer a high-quality quilters cotton with a softer feel. Art Gallery and a few other fabric manufacturers have incredibly soft cottons that are so soft on a quilt. I also absolutely love the colors of Pure Solids from Art Gallery. However, due to cost and availability I use a variety of other fabrics and solids. Mostly Kona cotton solids.
Basting:
I currently take most of my quilts to a long-arm quilter but I have on occasion had her baste quilts for me as well. She does those quickly and with a 1 inch basting stitch.
The only at-home basting method I like is spray basting. I use 505 to spray and only do this when the weather is good enough to take the quilt outside to spray. I also use painters tape to hold things down as I smooth.
Starch:
Don't starch pre-cut fabrics because they will shrink! Starching basically stiffens fabric to make it easier to cut accurately and can help with sewing and matching seams. It can shrinks fabric about 1/2 inch in one direction. That also means when you wash the quilt there will be less shrinking. I starch only when there will be a lot of bias edges on the block in order to prevent warping and stretching. I use June Tailor Savvy Starch. It has very little smell and although I react to a lot of starches, this one doesn't bother me. Note that if you starch the quilt top fabrics you may also starch the back of the quilt, this will help the shrinking of the fabric to be more even.
Needle:
A good hand stitching needle is different for everyone. Mostly because our hands are different sizes, so a different length of needle is more comfortable. A size 8 is usually good for beginners. I find I really like size 7, my hands are on the small size. You can get a multi-size pack of needles and try out the various sizes.