Someone's going to jump on you for it, so I might as well start by pointing out it's "Ithaca". The Ithaca Gun Company is one of the classic American firearms makers. William Baker was also associated with this company (Baker was the design guru behind the L.C. Smith and Baker patents, as well as having involvement in Ithaca). The model 37 is without a doubt Ithaca's signature model. One of the vintage you describe is certain to offer years of reliable service.
Adjustable chokes work on a principle similar to the aperture of a camera. Separate vanes close gradually from all sides to constrict the opening. The adjustable chokes from the era when they were most popular (coincidentally the same era when model 37's were popular, too) were not steel compatible per se. But, because they're adjustable, they can be opened up to the equivalent of "modified" or "improved cylinder" (speaking in lead choke terms), which are generally safe to use with the 2 3/4 inch steel shells that can be used with your gun. Unless I'm confused, your 37 is not chambered for 3" shells, and certainly not for 3 1/2".
Choke selection with these devices is accomplished by twisting the whole choke extension (or in some cases, a knurled portion of the choke extension) either clockwise or counter-clockwise, relative to the end of the barrel. When you only have one barrel, adjustable choke selection is a nice feature. Double-barreled shotguns will usually have a tighter choke in the left barrel than in the right, when not equiped with removable choke tubes. With double trigger doubleguns, this offers 'instant' choke selection simply by selecting the fore or rear trigger, depending on the target distance.
The absolute BEST way to see what the Herter's adjustment is doing, is to take a few boxes of shells out to a patterning board and to try each setting to see the effect of each adjustment. Once you know what effect you're getting, you can make informed decisions on what setting produces the desired pattern for the kind of hunting you'll be doing. Remember that you will get different patterns from different makes and types of shells. Steel shot, in particular, yields tighter patterns through the same choke as compared to lead shot. When patterning or shooting steel shot through your gun, start with a wide open choke and constrict only as much as absolutely necessary to acieve the desired pattern. At no time should you shoot steel through that gun/choke with the choke adjusted any tighter than "modified". To do so will almost certainly result in damage to the choke, the barrel, or both. In all cases, you should avoid using steel shot if you have a choice.
Edited to add: Yes, you can shoot slugs through it. Keep the choke wide open ("cylinder" setting) for this purpose.
