As many have posted, the part of your idea that involves getting a deli-top cooler is no good. Deli meat does not last that long in a prepped state, so unless you get real weird with your deli meat consumption it will be a big waster.
The deli slicer is a little more of a complex issue. I would love to have one. maybe will, someday. there is alot of stuff you can do with a good slicer beyond traditional deli meat. Anyway, I am sure you have noticed that deli meat prices are full retard. Apparently, slicing a meat into thin slices increases its value by 8$ a lb. So if you can find a way to slice your own meat AND get around spoilage issues, it could a money saver. Some deli meats freeze ok in a whole muscle state. So, you can get a big ham, cut it into 1 week portions, then freeze them. thaw for use. cooked hams freeze ok, as do most recon meats like deli "turkey."
Better though, is you can roast you own beef, pork loin (delis do not often do pork loin shaved for sandwiches, but its great), corned beef, ect. You will save alot by starting with a large or primal cut and roasting, portioning, freezing, and slicing to use. Example, decent deli sliced roast beef (as in actual beef) is usually 10-12$ a lb. You can get a rib roast for <5$ per lb, roast it prime rib style, and run that bitch through a slicer for a roast beef that will BLOW AWAY the deli stuff for half the price. Cheese, salami, and bologna is much cheaper when bought in log form, too. and don't even get me started on prosciutto, pancetta, and cappicola.
The big catch in this plan. Deli slicers are INSANELY expensive. New, commercial slicers go for thousands of dollars. You might find one for 800 in good condition on craigslist, but usually more like 900+. Dont be afraid of used equipment of this type, commercial appliances are an embodiment of workmanship( i worked at a restaurant that had an 80 year old stand mixer, still used every day). The $99.99 cheapo home units are garbage. awkward to use, low powered, and just not efficient enough at slicing to actually become a part of your family logistics (and hence, actually save money in the long run).
Maybe someday:
(i.e. maybe someday i will have 7k to throw at something as silly as a flywheel slicer)