I normally pad the jaws with some aluminum or copper and grab the least amount of stock I can and have it not flop about. Use an indicator and a "precision adjusting tool" and knock the end around to minimize runout. Then center drill it at 100rpm or so. Put a center in the TS and turn a band then flip it in the chuck and do it again.
This is the way to aproach this job if you do not have a 4 jaw independent chuck and/or the free end is true enough. Sounds like you have some pretty rough stuff.
If you do have a 4 chuck as deep as you can, indicate the free end best as you can, and center drill. As noted before you may get some chatter. Ignore that for now, we'll fix it later. Make the smallest center you can consistent with the needs of the part. That is, you can't make a tiny center on a huge part. Next, pull the part almost all the way out of the chuck so you can bang the tailstock end around just like above. Indicate stock at the chuck, then bang the free end in, go back and forth until both ends suit you. If the shaft is heavy make a pad flat on one end center hole on the other and jam it against the part with the tailstock. It will support the weight and make it easier to indicate the free end in while barely chucked.
Now turn the tailsock end on a center, can be live or dead. I prefer live. In general not as accurate but it is more practical. If you use a live center indicate the actual center as close to the work as you can get. If it wobbles a bit tap the work around until the center doesn't, else the center will not be on center. Now you can make your cut. If you want indicate the live center again before finish cut. The stock may have moved or stressed may have been relieved.
If the stock is small enough for the lathe bore you can finish the other end easily, if not do it in a simalar fashion to the first end.
If the center chatters AND the stock will pass through the spindle after first op just rebore the center. Small centers work better than big centers, I guess becuase there is less center there to be ugly.
Some of the posts mentioned steady rests which you said you didn't have. Get one if you can they are very handy. No use on rough stock but as one of the other posters said stick a collar over the shaft with 4 setcrews in it and, bobs your uncle, you have a steady rest journal.
Often and often will turn a dead center in the headstock chuck. Easy and quick and runs as true as your skill allows. Preference is to chuck and center. Just be sure the tailstock center end is running true as above. Chuck on a "hinge", a strip of shimstock or even a wire ring so the chuck is not emposing any incorrect angular alignment on the workpiece.
And nothing wrong with playing with rough stock. Forces you to learn some technique. We used to make hi pressure steam valve parts and some of the stuff was super special certified carbon steel rough forgings, supllied to us by customer and NOT rough turned. How rough was it? We called the forgings dog turds if that gives you an idea.
Enjoy your hobby. It is a great one. It's how I got started at 9 years old. I would never mention that around here, tho.
