Whatever you buy, make sure it is a metal base. The more steel the better. The plastic ones not only don't last, they put all kinds of static in your fabric.
Stay away from the new fangled computerized crap. Just more stuff to break and you won't use any of it. All you need is forward, backward, straight and zig-zag in various spi (stitches per inch). Make sure you can set your pressure foot tension -- that's because when you are stitching stuff that is thick you don't want as much pressure on the foot or you'll have trouble feeding through the fabric. Get at least one spare belt right away. Lastly, if you come across one with a free arm, that's easier to work with for blankets. All it means is that there is more room between the stitch area and the vertical housing on the right for the mechanical (belts) to the electric motor. But I have done king size quilt work on my normal machine.
If you plan on doing anything thick (like those blankets), make sure you practice first. There's a special touch needed to get those to work!
Singer is good and I have a a Nelco. I bought the Nelco because it's all metal and has just what I need and no more, plus had a 20 year warranty. When I had a problem, I called them up and they told me how to fix it over the phone. Great! I bought that machine in the mid to late 80's and it's still ticking along just fine! I doubt I'll ever need another.
New or used? Well, I guess that depends what you can find used. Some outlets will sell used ones that have been retuned. If it's a quality machine, that's fine. But if it's crap, well, then it's crap regardless if it's new or used. :)