I bought the common cheap chucks when I bought my lathe & mill, 3/8" and 1/2". The 1/2" is holding up fine after years of work, but the 3/8" has lost the gearing to tighten it properly. I've bought several keys hoping that would be good enough but finally gave up and bought a Jacobs. The key fit is so much better.
I also got tired of keying my tail stock chuck so I bought a keyless Jacobs and love it. I left the tang on my chuck adapter, and yeah, I lose about an inch. I left it on to pop it out easily. You don't really need the extra travel on a lathe, just move tail stock. Both of my Centers don't have the tang and are sometimes a pain to pop out.
Speaking of chucks, here's a Shop Tip. I recently had to do some long-drilling for a home remodel project and instead of buying a special long drill (just price one), I bought a very small diameter 1/4" chuck with 3/8" X 24 thread mount for about $10. I also bought a 3/8" of the same. With a 3' length of All-Thread, you can make it a long as you want, or cut it up for several different lengths.
Buy quality chucks or be sorry that you didn't!