Dear Mary II,
I have a few recommendations:
1. Go with a known brand. Bernina, Viking, Husqvarna, Pfaff, and Singer (with reservations) are some that are known for quality and have been around for a long time. I've used all of these at one time or another and been pleased with them (my current machine is a Singer CG-550, and I love it.) To save money, you can buy a better-brand sewing machine used. Some tips are here
2. Things to look for in your machine might be automatic tension adjustment, easy bobbin threading, free-arm sewing, easy button-hole feature, and number of stitches (you'll want straight and zig zag, but you may want to forgo more fru-fru ones to keep the price down.)
3. Go to a fabric store and ask them for recommendations. Even if you don't buy from them, you can see and try out lots of different machines and figure out what you're comfortable with.
4. In Provo, they often have school surplus sales at sewing stores in the area. These are heavy-duty machines that aren't really fancy, but are designed to hold up through lots of use. That's where I got my machine, and it's been very good to me. You can call around to local stores and see if they can tell you when their next one will be.
Hope this helps.
The Cleaning Lady