All wonderful advice!
I took four years of sewing in high school and it was always drilled in to our heads that you always back-stitched at the beginning and end of every seam. That was such a tough concept to get over when I started quilting. I kept hearing my Home Ec teacher's voice in my ear yelling that I didn't back-stitch.
For little starter pieces, I tend to hold on to the triangle pieces that I trimmed while making my binding from quilts. Since I acquire so many of those pieces, I just use them a few times, then toss them out. To the OP, using a leader scrap of fabric is extremely useful whenever you are making half-square triangles or sewing anything that may be on a bias or starts at a point. As you may have already discovered, sewing machines tend to eat those innocent little points!
For a first project, I would really recommend that you do alternating squares to make a baby quilt. Gotta start somewhere. If it turns out nice and you have no babies to give it to, look for your local Project Linus group. They will find a baby that will love it!
Even the best of us occasionally get our 1/4" seam a little bit out of whack. When I see it happen to me, I quickly stop and cut my threads. I will put my needle back down about an inch before my stitching went wonky and simply start stitching again from there.
Lastly, know that quilting is quite addictive! Unless you have a lot of time and money for fabric be sure to stay away from the Missouri Star Quilt Company quilt video on YouTube!!! Just kidding. I discovered their videos this summer and LOVE to watch Jenny create something new. They have several beginner videos that you may find helpful if you haven't already watched some of them. Vanessa from the "Crafty Gemini" also posts a weekly tutorial on either sewing, cooking or gardening. Most of her sewing/quilting videos are really aimed towards a true beginner. Good luck in your new quilting ventures.