Frozenmama,
They don't make a simple machine with just straight and zig zag stitches any more. I have Singer 237 that only has 2 stitches, course its almost 50 years old now and heavy. Most sewists don't use more than a few of the decorative stitches that are standard with their machines.
To get anywhere close to the machine you're describing, the Husqvarna Viking 118 is the only one I can think of; don't know if its still made. The 118 is mechanical, has needle up/down,adjustable needle position, 18 stitches.
I used to sell new HV machines, its a great machine.