Bruce,
Congrats on the new lathe. Hope you enjoy using it. Is this your first foray into turning? Be sure to holler here if you need help. Also, look in the club listings here to see if there is an AAW turning club near you. Hands on help is a wonderful way to cut the learning curve down to size.
For a small chuck, you need to know the thread size of the spindle on your lathe. The manual shoud say. It will be given in terms of the diameter and the thread count. For example, 1x8 would mean 1 inch diameter and 8 tpi or Threads per inch. Then either go to a nearby store with turning supplies, or use a mailorder shop like Craft Supply USA or Packard Woodworking or Woodcraft to order a chuck that will fit that spindle.
I suggest a chuck with interchangeable spindle inserts. Some chucks have the threads for mounting on the spindle built into the device. Other chucks have no threads and instead accept a spindle insert that has the threads on it. That way if you eventually upgrade your lathe to a larger unit (most of us do at some point in our turning careers) then you do not have to go out and buy a whole new chuck to fit your bigger lathe. You just pull the old insert out and replace it with one that fits your new spindle size. This versatility might allow you to buy a higher end chuck knowing that it will last you through many lathe upgrades.
I just recently bought a small Jet Mini lathe to use as a traveling lathe for demos and classes. (I hauled a big 450 lb Jet 1640 to a demo once. Not eager to do that again!!!!!) Anyway.....I bought a small Nova (technatool) G3 chuck with a 1x8 insert to fit it. Technatool has a decent reputation but for this partricular unit I was disappointed in the quality control. I should have just returned it to Woodcraft Honolulu but I had it in hand and fixed the issues, which were many, and now it works fine. I did let Woodcraft know what I found wrong with the unit by the way. Anyway....I like the size of the G3 in relation to the Jet mini, and assuming you did not experience the quality control issues I saw it would be a good unit and reasonably priced. Like most good chucks on the market these days it has replaceable jaws for different purposes. My other chucks are all Oneway Strongholds, pretty massive for a small lathe but perfect on my 1640, and they have all been nicely built. No problems. I have never used the smaller Oneway Talon chuck, but it looks very nice. You will also see Axeminster listed in our US catalogs and they are excellent units as well.
A question for the rest of you out there using small lathes????? What are your favorite chucks?
Now....a question for you. I assume you bought the Sears lathe because it was a small lathe and was probably an inexpensive way to get started and see if you liked turning? If that is the case and you envision stepping up to bigger and better lathes some day you might be able to save some money by using alternate ways of holding your work. Jam chucks and face plates and pin chucks and what not all work very well and cost alot less (or nothing at all) compared to a good 4 jaw chuck from Oneway for example. Using some of these alternate methods might cover your needs until you are ready to move up. In the meantime, put the money you saved on chucks into a piggy bank towards the big lathe later on? Just a thought.
Hope you have a blast with your lathe! You will probably find it as addictive and satisfying as the rest of us have!!!
Dave