Most often the cause of a machine problem is the needle. There are a myriad of needles to choose from and the issue can get overcomplicated. One key point is that as the number gets smaller the needles do too, unlike threads.
The advantages of leather (for leather, makes a neater hole) or ball point (for knits, does not cut the threads in the fabric, so no unraveling) needles are obvious, but a good-quality SHARP regular-point needle will sew almost anything you can put between it and the needle-plate. Note that’s SHARP, as a blunt needle will destroy your cloth, your work, your thread, and your temper, in exactly equal parts..
It’s important to match needles and threads for size - a needle that is too big or small for the thread will make a poor tension in the stitch and a too-small needle will cause breakages and fraying. For piecing I use a fine thread, 50 cotton or similar, and a size 12/80 needle, for silk an even finer thread and a needle of size 10/70 or even 9/65. The good news is that some needles are now colour coded so no need to reach for the magnifying glass! If you have a favourite brand/size buy in bulk - it is so much cheaper.
Many really old machines are hard to find needles for, but the Singer 15x1 (also called 2020, HAx1, and System 705) has become the domestic machine standard since the turn of the 19th century. Industrial machines use an incredible variety of needles sizes and types, more than 5000 different sorts are in common use, plus a whole lot more for specialised purposes.
When sewing machines were a new idea, needles had to be adjusted every time to make sure they stitched - and they were expensive. Now, needles are cheap, easy to find, and made extremely consistently, so no adjusting.
So, how about you changing yours? Needles should be changed about as often as underwear, that is, after 8 - 10 hours of use!