Most of the old Atlas lathes that I'm familiar with have a 1 inch by 8 tpi head screw.
BUT, Atlas made many, many different lathes (for many vendors) and the headstock on yours MAY BE DIFFERENT!
a quick, inexpensive test is to purchase a 1x8 nut at the hardware store. This nut should be cheap and it does 2 good things for you.
First, if the nut fits the headstock nicely, you'll know that you have a "standard" 1x8 headscrew and a 99.9 percent chance of having an MT2 taper underneath. If the nut is too big, that likely means a less common 3/4 inch headscrew and a MT1 taper. If larger, a 1 1/2 headscrew and a MT3 taper.
Second, just by gently starting the correct sized nut onto the headstock, you can "go easy" and feel any thread burrs that can be cleaned up before damaging the threads on a new chuck or adapter.
As far as inexpensive chucks, I highly recommend the Nova chucks simply because they seem to run a little smoother than other brands AND all Nova jaws fit all Nova chucks. This is NOT the case for many other lower end chucks.
The opinions of the membership on this question will likely be as diverse as the membership here. These are just merely my observations and recommendations.
Respectfully submitted.