Mike, for call making I would get any of the lathes mentioned, Jet, Delta, Turncrafter and I am sure there are other good quality clones of the Jet, most are made in the same Chinese factories, just different inspectors and configurations such as switch placement. You really want a lathe threaded 1x8 tpi headstock, #2 morse tapers in the tailstock and headstock. I wouldn't go Craftsman, unless they have something new I haven't seen yet. It will run you a little over $200-400 for a good starter lathe, most of the guys like variable speed, mine is not Delta LA200 but it is a small matter to shift a belt and I use two speeds most of the time, so if you want to save some money you don't absolutely need variable speed. The Turncrafter Commander has variable speed for $300, 3/4 hp,might be worth looking into, however I haven't seen any reviews. Most of the mini lathes have 1/2hp and I wouldn't want any less.
If you want a lathe that will last a lifetime and perform perfectly, there are always VicMarc, Powermatic,Oneway and Nova lathes, these are more than most would need for call making, the VicMarc VL100 however is one I would love to have. Matt McLain has one and could tell you more about those, it is a very smooth and accurate machine and sturdily built with roller bearings, designed to last.
You will probably want a four jaw chuck depending on how you approach whatever call you're making, I run a Baccacuda2, it comes with 4 sets of jaws so a lot of bang for the buck, $170 from PSI, they aslo have them on Amazon.com. There are other 4 jaw chucks that are maybe better, but I like the one I have. You will probably want a Jacobs Chuck with Morse taper to fit your tailstock. For turning tools, you might watch E-bay, sometimes you can get some good deals there, and your going to need a sharpening system of some kind, another whole topic in itself. I use Benjamin's Best and older Buck chisels, just make sure you have a decent 3/4"gouge, skew, round nose scrapers,v scraper, parting tools, good tools can be expensive, you can also get them one at a time. You will have more in accessories than in the lathe more than likely, but you can buy what you need when you need it
If there are call makers or woodturners in your area, it might pay you to spend an afternoon picking up some pointers from someone with experience, and always when working around a lathe think safety, no loose sleeves, and so on. There are also a number of wood working and turning forums on the web, just google them and spend some time checking some out, such as Sawmill Creek. There are also a number of you tube videos on turning, demonstrating cutting and scraping techniques. Most guys start out scraping but if you learn cutting tecniques, your work will go faster and a nicer and smoother finished product, resulting in less sanding and frustration