You need to decide what your budget is for a new machine and what else you want it to do besides sewing through denim. Many of us here have older machines (prior to 1965 or so) that have metal parts whereas many modern machines have plastic parts and simple do not hold up well over time.

If your budget is sufficient, I always recommend the Husqvarna Viking machines that are made in Sweden. The Bernina brand from Switzerland is also excellent. An older 15-91 Singer model might be found at a thrift store for less than $100 plus the cost of a tune-up and a replacement electrical cord if needed. These older Singers may still have a lot of life in them yet. Also look on Craig's list for older machines.

Check your local fabric and sew/vac stores for used machines - let the salesperson know that you want a heavy duty model or one that will sew through denim.

After taking a "quiz" put to me by my friend's DH on current sewing machines in Consumer Reports, I found out that a basic Kenmore model can be had for $120 and it was recommended for basic sewing for beginners. It sewed well through shear fabrics for curtains as well as much heavier fabric.

Teresa

I second the recommendation for a Husqvarna Viking machine. I've had mine (Model C-10) for about a year, a replacement for my beloved 1961 Singer. (In between I also had a Kenmore, circa 1978, that never performed well). The Viking sews all thicknesses beautifully and feels solid and well built. My only regret is that I didn't get the C-20 model which has more applique features.

How much could one expect to pay for new Viking basic sewing ? How about a basic Bernina?