Depends on how you want to chamber, the lathe's condition, and it's bed length.
I have a SB 9 (among other lathes) in very good condition that I rebuilt (DRO, VFD) that I've cut very accurate chambers with between centers, but you need the bed length- mine has the longest made at 4-1/2' and is the minimum needed with about 32" between centers. I run either a Jacobs Rubberflex Collet chuck, or a 6-jaw Buck Adjust-Tru on the spindle, both have less than two-tenths runout.
It's laughable that the "know-everything" crowd crows that you can't cut a decent chamber between centers on a 9" SB when in fact, they were commonly used. I'm staring at an article written by a benchrest shooter for Rifle magazine using a SB9 to chamber his barrels. Sure, it was 40 years ago- but what worked then still works; provided the operator and the lathe are up to the task.
Sort of ironic that one of the first paragraphs reads:
"There is no one correct way to catch a fish, train a dog, or chamber a rifle. Every gunsmith has his own approach, and most have a lot of good reasons for feeling that their method is far superior to any other and that every other gun mechanic in the world is still groping around in the dark ages. This all makes good bull-session material, but the important thing is that in any quality job, certain things must be done, regardless of the method used".
If you want to chamber through the headstock, the SB9 is not an option- nor is it a viable option for working between centers if it has less than the 4-1/2' bed for all but short barrels. I use my 9A when I work between centers, and a bigger-bore Sheldon when I want to work through the headstock. Both methods work, and I choose which method based on the requirements of/type of rifle being built.
Problem with older American iron is that because of their age you need to be able to determine whether it's too worn to be able to turn out accurate work. Value for that SB could be anywhere from hundreds to over a couple grand if it's in good condition without excessive wear with a good amount of tooling.
McMillan, Kelbly's, and many others still chamber between centers. Working through the headstock with a spindle bore large enough to do so allows you to get by with a short bed length which is an advantage if you're tight on space. To work "both" ways, you should have 36" between centers, and minimum 1-3/8" spindle bore for 1-1/4" barrel blanks.
"Rigidity", IMO, is relatively unimportant when it comes to working on 1" hollow steel tubes...important for a job shop- not so much in this application. Any lathe needs to be tight, and in alignment to do this work- and I'll take a bechtop lathe that's tight and accurate over a 3,000 lb hunk of cast iron that's clapped out and incapable of turning without a taper or can't hold a thousandth.