First off, what is the spindle bore on your machine? Or, if you want to hold work a little larger, what size do you want to hold? That determines what size range you want. ER32 and ER40 are commonly used around here, 5C is pretty popular as well. They all have pros and cons, so you need some idea what you want to use them for before deciding on a set. Do you have or plan to get a mill, or is this just for your lathe?
It sounds like you are thinking to use end mills or other tooling on your lathe spindle. Do you know what type? There are a couple ways to do this, but it's important to make sure the tool can't "walk" out. So you need a drawbar setup, do not hold them in a 3/4 jaw. And end mill will want to pull into the work, you need to make sure it can't do that. Also find out the torque requirements for the collets you use. It's surprisingly high for some of them. Make sure you have a wrench for them. Note that collet chucks often do NOT include one.
For tool holding, a higher quality set is recommended. For work holding, it's less important. Though I wouldn't recommend the super cheap set from Banggood and the like. I've seen some reviews on them that make me wonder why one would ever buy them.
How the chuck attaches to the lathe depends on the type you get and the type of lathe. For the direct spindle type, your spindle likely has a morse taper, MT3/4/5 probably. You remove the chuck, place the collet chuck in the spindle taper, and use a drawbar to hold it in place. Then you can install collets with the work or the tool. Note that drawbar style holders generally prevent using the spindle bore to pass long material through. That's not a problem for tools, but it might be for work depending on what you want to hold.
I believe your lathe is a bolt on style chuck. You could make an adapter plate for a more "standard" looking collet chuck as well. My lathe chuck is this one.
http://www.shars.com/5-er40-zero-set-fine-adjustment-collet-chuck ... It works well for me. To mount it, you also need a backing plate that matches your lathe's mounting system. Mine uses D1-4, so it's pretty simple. Yours would likely involve drilling and tapping holes to hold the backing plate, then bolt the chuck to the plate.
Do not attempt to use a collet without the correct collet holder. Clamping a collet in a 3 jaw will just destroy the collet. I have heard of people using collet blocks in a 3/4 jaw chuck as well. I have no idea if this is a good idea in practice. I imagine a 4 jaw with a square block could be indicated in and work well. A hex block would probably work in a 3 jaw, but it would only be as accurate as the 3 jaw. So I'm not sure why one would bother.
Honestly though, the question to ask is "do you need collets?". They make some things faster, but there's not much you can do with them you can't do with a normal chuck. The biggest advantage to me is the ability to work in close and to use gravers later. And I can hold finished parts without maring, but you can use aluminum shims or similar to do that. Setups are more reproducible, but a 4 jaw can do the same, just a little slower. If holding end mills is what you're after, it's much cheaper to use an end mill holder with a drawbar in the MT spindle taper.
