I have a Janome Heart Truth which is awesome, but it might not be a beginner machine. I've heard amazing things about the Hello Kitty Janome
machine. It's basic, but it has very few issues. You can also buy it without Hello Kitty on it, just look for the model number and they make a plain one.
Honestly, I wouldn't buy a cheap Brother machine. I had two when I was first starting out and just wanted something inexpensive. They both broke ridiculously easy and were so hard to use. Second hand is a good idea to cut down on costs, if you check dealers and things like craigslist. Just make sure you can try it out before you buy so you know it works!