Welcome to the board and to the wide world of quilting. I hope you enjoy your time with us.
You don't need much really for a sewing machine. Many of us love our vintage machines with a good steady straight stitch. For the last couple of months with Covid going on both my vintage and my expensive machines were down, and I was sewing on a bottom of the line Brother, probably cost less than $100 or close new. It did just fine to keep me going with masks and such but I'm glad to go up in power. I was surprised that my machine was so low end, there was on minimal ability to change the stitch length -- so I now know to mention that in addition to however many stitches they say you can make, look to see how short/long or wide/narrow they can go.
On the other hand, for several years I sewed on about a $300 Brother I got from Costco and it was a pretty good plastic machine. They aren't designed or meant for heavy lifetime use. My expensive machine is a Bernina, and it was given to me after about 10 years and 2 previous owners -- it retailed for closer to $10k, and still sells for $2-3k, the repair bill was $250 which is closer to what I'd usually be looking at to buy a machine, not repair it. But heck, this machine cost about as much as my car did and was definitely worth the repair. So there is no real answer except to start with get something you are comfortable with, both in price and operating features.
As far as the quilting, I am self taught, took me 40 years to get me to where I am today. Today we have the internet and videos even! But basically it boils down to we put two pieces of fabric together at a time and go from there. Eleanor Burns Quilt in a Day books are a good way to get started. Keep in mind that there is hand/eye coordination as well as design sense and physical material issues, so we don't usually start out with a marathon but some small baby steps.
If you were my beginning quilter, I'd start by turning over your mat so you cut on the side with no lines from the beginning. You use your ruler, not your mat lines!
And then I'd make you do what I call "driving lessons" sewing lots of boring strips together until you get a consistent 1/4" seam allowance (or whatever allowance you use, 1/4" is standard for directions and patterns).
Something like a "jelly roll race" would be driving lessons and result in an actual project. You can buy the precut strips even.