FR,
If the 11-56 is an 11" swing machine, then AXA size is most likely what you want. It depends upon the vertical distance from the top of the compound slide to the spindle axis. The BXA size is too tall for most 12" machines so it would probably be too tall for an 11". The criteria is that when properly adjusted for height (cutter on center), the bottom of all of the tool holders should be at least slightly above the mounting surface on top of the compound. In other words, you want to be able to clamp down the tool post at any angle relative to the compound and anywhere on top of the compound.
Check the width of the T-slot on your compound against the diameter of the bolt or stud that attaches the tool post to the compound and make sure the bolt/stud will go into the slot. The one thing that you may have to make or modify is the T-nut for attaching the tool post to the compound. One usually comes with a set but it may or may not fit the T-slot on your compound. The only other modification that I've ever heard of was on all Atlas 10" compound slides. When the factory machined the compound slide casting to make the flats and T-slot, they only machined back far enough to clear the lantern tool post that was once standard on all lathes. The AXA TP is wider than the lantern one. And the corners of the AXA hit the surface where the factory quit machining. So people with these machines have to machine the flat farther back. On most machines, this isn't an issue.
As to piston or wedge, the price difference between them in most brands today is usually less than the cost of one or two tool holders. Plus most of the Chinese made ones have small cylindrical pistons instead of the larger rectangular ones like my 35 year old Yuasa has. Unfortunately, the Yuasa is no longer made. So I would go with the wedge type, and not the cheapest one that you can find, either. You don't want to ever have to buy another one for the machine you are putting it on.
AFAIK, Shars has a pretty good reputation. And whatever you buy, be sure that you buy at least 5 extra 101 Facing & Turning holders and/or 102 Boring, facing and turning holders. The standard sets usually come with one of each. Once you get a cutter installed in one and set on center, if you have to remove it and install a different type of cutter, that you have to then re-center, you aren't much better off than with a lantern style holder. I have 11 of the holders, and 9 of them have some type of cutter installed and centered.
Also, although it costs about twice what the simple 101 holder does, consider buying one #116 type holder. This holds two triangular carbide or HSS inserts, one for turning and one for facing. About 80% of the time, that's the holder that I use. But the thing to look out for in a 116 is at what orientation the insert sets. I have seen them two ways. The preferred way is with a long side of the triangle parallel to the length of the holder and perpendicular to the lathe axis. With this, you can turn up to a shoulder. I've seen at least one make where the triangular insert was rotated 30 degrees CW such that a long side of the triangle would be toward the operator and parallel to the lathe axis with the tool post in its normal orientation. To use it, you would have to rotate the tool post 30 degrees CCW.
All that I know about steady rests is that you buy the one that fits the machine.
