Don't get me wrong, I loved my 40 year old Kenmore sewing machine, but the years of neglect it went through before my parents rescued it from a yard sale took their toll on it.
I feel very lucky to have had that as my first sewing machine. It gave me a better understanding of a sewing machines workings then I would of had if I had a brand new sewing machine right away. Which is why I've handed it down to my sister in hopes she'll be able to use it and love sewing as much as I do.
The first project I did with my new machine was to take an old pair of office pants and turn them into a pencil skirt. I think it turned out pretty well.
I opened up the inseam of the pants and sewed them together, then hemmed it. Not the most intense project but the sewing took less than 30 minutes which would have taken over an hour on my old machine.
edit: Check out my new post How to Make a Pencil Skirt from Pants for instructions on making this pencil skirt.