I have a Singer and Brother. I do love my old trusty Singer, it wasn't expensive (around $200) and it works great. The Brother machine was about $200 also and works great, but it's not my favorite machine. It's computerized so it acts differently. We have a sewing group that meets once a month and lots of the ladies have Brother machines and LOVE them.
As for projects, the best ones will be the ones you are personally motivated to make for yourself or someone else as a gift. The first thing I ever sewed was a pillowcase. It's about as easy as it gets! Other fun easy things are pouches, simple purses, aprons, place mats, cloth napkins, square block-style quilt blankets or table runners, or adding decorative applique to towels or burp cloths stuff like that. Some small plush projects can be super easy, too. Like those Ugly-Doll inspired monsters and things. Just search Etsy or Pinterest for "easy sewing pattern" there's also a lot of free tutorials out there on blogs.
