My initial search led me to a lot of sites talking about Polyvinyl Chloride or PVA based slime. These sounded like a good way to make slime, until I realised PVA is expensive, isn't available in your corner store, is colorless, and makes a slime which is more rubbery than mucus-like.
Most sites suggested substituting Elmer's glue, because it contains PVA, but Elmer's glue only comes in either white or clear, and is likely to harden. Not something you want on your suit, and not particularly realistic looking.
But then I found out about another kind of slime, which can be made more mucus like and which is even the right color. And supposedly, according to one site I found, it is the very type of slime used in the movies.
It's called Guar Gum slime, and it is made by mixing Guar Gum, a common thickening agent used in baking, which you can find in any health food store, and Borax, a detergent which is available in any supermarket. (Borax is also the second ingredient used in PVA slime.)
I've mixed a batch myself following some fairly loose directions I found on one site not particuarly carefully, and it's very promising. I haven't got the recipe quite right yet, having inadvertently used about 10x as much borax as I was supposed to for the first couple tries, but it's definitely mucus colored, and slimy and the ingredients cost about $12 and will make BUCKETS of the stuff.
Here is a scientific paper on how to go about making it properly the scientific way:
The directions I followed used cups and teaspoons for measurements but since I haven't made a completely successful batch yet with those I can't reccomend them.
Note the mixture does have a bit of an odor to it when you use the heating method. But I didn't notice an odor when I tried just making it with cold water, so the borax odor probably goes away when it cools. And speaking of cooling, you need to keep it in the fridge or else it will get moldy in a week. One site suggested adding a few drops of lysol to help prevent this, but since it'll keep in the fridge for a long time, there's no real need for that. Also another site said it would break down after a few days anyway. Perhaps they didn't use distilled water though, I don't know. The scientific paper says to use distilled water for that very reason.
Well, good luck making your slime. If you want easier directions to follow just search guar gum slime on google, there's plenty of pages about it. And post your recipe if you get that perfect mucus-like slime that oozes but doesn't run right off things.
Oh, and if you do want PVA slime, the easiest way to get it is to buy a kit from here:
They have the same kit in green too. But remember, this slime is supposedly more flubber-like than mucus-like.
Oh, and I just realised that the borax smell I noticed would also be greatly reduced if I didn't use 10x as much borax as I was supposed to.