The vast majority of your lathe work can be done with jawed chucks. Keep the following in mind, Dave:
A first operation is when you take some stock and turn it for the first time. For this kind of work, which is how most of our work starts off, any scrolled chuck (3, 4 or 6 jaws) will turn the work dead on the centerline and will be accurate as long as you do not remove it from the chuck. This is true for cheap chucks or expensive one. The difference between a good one and a junk one is the quality with which the scroll and jaws are made and fitted. The better chucks have more precise machining and will grab the work better. Given that the vast majority of your work will be done with a 3 jaw, it pays to have a good one.
A second operation is where you are turning a piece that has either already been turned or is precision-ground. Here, you need a 4 jaw chuck if accuracy is important. An independent 4 jaw chuck is potentially the most accurate of all lathe chucks because you can dial the work in for zero run out. It is also the most versatile because you can adjust it to turn off-center work or work that has an odd shape.
Collet chucks come in last for lathe work holding. 5C is good for production work where you have to run a lot of nominal sized stock. ER chucks are good for holding threaded or already turned parts with fairly good accuracy and they are faster to use than a 4 jaw; they are accurate but not as accurate as a 4 jaw.
6 jaw chucks are another variation you'll see. These are scroll chucks like your 3 jaw but they obviously have 6 jaws. They tend to distort thin walled work less than other chucks and will hold any work more solidly because there are no large gaps between the jaws like a 3 jaw has. They are especially good if you work with a lot of plastics because that material tends to be slippery and can cam out of a 3 jaw when taking big cuts; a 6 jaw holds this material more securely and therefore more accurately. Most good 6 jaw chucks tend to be the adjust-tru type so they can also be dialed in to be very accurate. While more expensive, these chucks are typically made to a higher quality standard by companies like Pratt-Burnerd, Bison and others.
Another variant is the adjust-tru 3 jaw chuck. These are just standard 3 jaw chucks but have 3 or 4 screws that allow you to shift the chuck around on its backplate to dial out run out. It is sort of like having the adjustability of a 4 jaw chuck with the speed and ease of use of a 3 jaw chuck. Good ones can be dialed in to be very accurate. You will find these all over ebay but be warned that many of these old chucks are beat up. The jaws and scrolls are worn and no longer accurate but because it is an adjust-tru, the seller thinks its made of gold. If a chuck looks old and well used, it probably is and you should keep looking.
I try to steer the new guys towards buying good chucks to begin with. A good one will last you a lifetime and will perform well every single time you use it. A cheap chuck will not hold up nearly as well or as long. Bison makes good ones that are a bit expensive but will hold up to heavy use. Rohm is my preference but make sure you're sitting down when you look at prices. Pratt Burnerd is probably one of the best out there. Yuasa is also very good. Kitagawa and Samchully are high end and out of reach for most of us. There are many others. If you find one you want to buy, ask the guys and they will give you an opinion.
Made a backplate to adapt it to my lathe. For me it was a waste of time & money. I've had it for a number of yrs now & I've only used it like twice. For the stuff I do I just don't need one, my chucks cover mostly everything.