You've received some great suggestions so far.
My first quilt was a rag quilt (actually my first three) which is more forgiving than many pieced quilts - mainly because your seam flaws and oppsies are largely hidden.
From there, I moved on to teaching myself to quilt using Harriet Hargraves Quilter's Academy series. I've since joined a local guild and take advantage of workshops whenever I can to learn new techniques.
Is is possible for you to test drive a few sewing machines? Have you ever used one? I grew up using my mother's 1960's Singer - fabulous machine, but very heavy. So when it came time to move out on my own, blindly/blithely picked out a new Singer (1990's base model). Boy is there a difference. I keep meaning to donate that machine as we have never gotten along.
As I started researching machines, I decided to look for 80's era Berninas - and now have an 801 and an 830 as my go to machines for piecing. These are solidly made and the ones I found on eBay and Craigslist were generally well maintained.
I also have a Brother PC-420-PRW, which is barely out of the box - attractive to me for the alphabets and decorative stitching - and the blanket stitch for applique work, if I need/want a good blanket stitch.
For quilting, I have a HQ Sweet Sixteen, and recently picked up a 1950s Featherweight for my son and I. He currently has a bit of a love-hate relationship with it, but I think they will develop a good friendship in time.
There is a huge variety of machines to choose from, depending on what you think you would like to do. Once you choose a machine, take a look at local quilt stores to see if they have a basic class - ours is "Get to Know your Machine" where we make a simple project to become more comfortable with the machine. It was not brand specific.
I've done a little hand piecing and agree that it is a great take-along project.
Welcome and Have Fun!
Cheers, K