Store brands tend to be just fine, more often than not. I've had hit and miss experiences with instant potatoes. I find the namebrand potatobuds just taste better. Dunno why.
Canned meats I sometimes question if the meat is processed properly, given the low price. (and how sometimes it smells or tastes a little off on the discount brands) I haven't been sickened or anything, I just question the quality of the product.
Vegetables? Generic store brand all the way, except again-- for things where processing is real important, like mushrooms.
Given then "Limited to slow cooker food only, must be dry goods only, limited shelf space, try to have healthy diet" nature of this conundrum, I would obtain:
Dry goods:
Powdered milk (Useful for a number of milk based soups, and provides a decent amount of animal protein and calcium. Normally you would need leafy greens for calcium in good quantity, and those dont store.)
Powdered egg (If you get those silicone boiled egg mold things, you can make knock-off boiled eggs, which make a good texture addition to things like ramen. It's also a naturally balanced protein, so don't knock it.)
Powdered butter & cheese (Mostly for the flavor function; you are gonna suffer large not having refrigerated food products on the menu, flavor wise.)
White and brown rice
Dry beans (several varieties)
Dry peanut flour
Pasta (whatever floats your boat, but I would go for whole wheat for the fiber.)
dry barley pearls
cornstarch (You will want a thickener to go with the cheese powder, for many of the cheesy soup types, should you attempt them in the makeshift slow cooker. For example, you could use powdered milk, powdered cheese, cornstarch, and canned spinach.)
Instant potatoes
quickoats
sugar
salt
Dry fruit (for the oatmeal; try to get it with reduced sugar)
Canned vegetables:
Whole kernel corn
Peas&carrots
Potatoes
Mushrooms
Asparagus
Green Beans
Black Olives (sliced)
Tomatoes
Tomato paste
spinach (You will need the vitamins in them. Honest.)
Canned meat products:
Spam (cheap and effective)
canned ham (Useful for vegetable soups)
canned chicken (also useful for soup, but don't expect amazing flavor.)
Canned tuna
other bottled/canned items:
Vegetable oil (I'd go with avocado, despite the price)
sesame oil (don't knock what it can do for some kinds of ramen, or other pasta. A little goes a long way-- its a flavoring, not a nutrition source.)
Spices (Parsley, Curry, celery salt, etc..)
Tahini (again, it adds so much to many kinds of soup. Another flavoring; shelf stable)
Bullion (I suggest knorr, and discourage getting a knockoff here. Not if you want food you actually want to eat.)
A quality multivitamin (because you really WONT be able to have a fully and completely balanced diet with dry goods only.)
That should give you quite a wide palette to paint with, despite your restrictions.
Some tricks can be done to heat the canned vegetables, such as heating them in their cans. (Peel the label off the can, put the whole damn can into the wide-mouth thermos, pour the hot water over the top, put the lid on. Let sit for awhile, then pour off the water, and open the can while wearing an oven mitt-- Do whatever with the heated veg. It might take more than one shot in the thermos to get the temperature you want.)