Cleavers are several different worlds unto themselves. They come in two basic flavors - the western cleaver and the asian cleaver. Whatever you might think, the two are vastly different in what they are and how they are used.
The western cleaver is all about brute force. You are looking to really whack something. It's a good way to work off aggression. The basic process is to mightily swing your your arm down from on high to gain momentum. Size and weight matter here. Good western style cleavers are thick, big, heavy monsters of mass destruction. A good example is the Dexter Russell S5288 - which one reviewer notes weighs 2.75 pounds. Yes, it will crunch through chicken bones. It will also crunch through and separate your fingers from your hand (or chop off your hand entirely) if you don't pay attention to what you are doing.
You will also need a good chopping block/table for these brutes. Figure a stand-alone table with a 4 inch thick edge grain maple block. Anything lighter is at risk of damaging your work area underneath or slamming right through plastic or wood to the work surface below.
Asian cleavers, more properly called broad knives, are often mistaken for European cleavers. However, they are the asian version of the chef's knife and in the hands of an experienced asian chef are able to undertake almost any task, including delicate work.. They can be found in very thin versions, with edges which are as close to a razor in sharpness as anything else you can find. They are superlative for fine, thin slices. It's not unusual for these knives to be single bevel. Good brands are CCK and Ho Ching Kee Lee.
Whether you need either type is a different issue, though. Each is somewhat overkill (from different use perspectives) for chefs, especially if you already have a good chef's knife (especially the MAC Pro Chef Knives).
If you want a separate knife for use by your guests, then an 8 inch Victorinox/Forschner fibrox handle chef's knife is probably adequate as a secondary knife, though a 210 mm Tojiro DP, a Fujiwara FKM or Richmond Artifex would be a step above.
I've been often enough in at Ross, T.J. Maxx, Marshall's, etc., etc. to pretty much not want to bother buying any knives from that type of store. The offerings are of steel which is of a quality below what "BDL" called "crap steel". They will be very difficult to properly sharpen and will lose what sharpening they do get very quickly. Better to go to a restaurant supply store, or biting the bullet and going online for one of the above knives.
What I don't see from you is any information about your honing/sharpening routines. If you don't already have one, a good quality hone (such as the 12 inch Idahone) can start the process of self-sharpening. You also need either some stones or a jig (such as the EdgePro) to truly keep your cutlery sharp.
Also, go to your local public library system and read Chad Ward's 2008 book, An Edge In The Kitchen . The basic information is good, though prices are long past any semblance of up-to-date.
Otherwise, just buying more knives is little more than a temporary sop before you need that "next knife".