Bicycle Tutor

Both front and back brake cables snapped (worn out, I think) and looking around for replacement cables. I have seen "generic" cables that say something like it works on "all models" etc. (those found at supermarkets, etc., mostly from Bell) and the ones I can find at the REI also seem to be pretty generic. But I see that there is this round thing at the end that keeps the two branches of the cable together, and those generics don't have those. I also realize that the Altus lever does not have the slot that would normally be used to remove the cables off the levers. Am I supposed to find some kind of non-standard (i.e. expensive) replacement cables for this seemingly common (Shimano, the de facto global monopoly) brake, and if so how I find it (e.g., stock number, etc.)?
Thanks :/

Any standard mountain bike brake cable should work. There are "road" and "mountain" cables with different end pieces (and then "universal" cables that have both). Mountain cables have a barrel shaped end with the wire coming out of the round side of the barrel.
If your cables are that old, I'd probably change the housing as well if possible. Also, I would buy the absolute cheapest ones you can find. But don't get talked into some super expensive ones. Good mid-priced cables from REI should work great.
good luck

You say that there is a round thing that keeps the 2 cables together?
I assume you mean this:=
http://www.sjscycles.co.uk/product-Shimano-Shimano-C-Type-Direct-Cable-Fixing-Straddle-Wire--Each-9360.htm
If you look closely you will see that the cable goes through one side and should be loose. Disconnect the cable at the cantilever and it should pull out through the round part. You then fit the new cable through the "sleeve" and reconnect to the cantilever.
Some generic cables come with a different "bullet" on each end. You cut off the one you don't want and then feed the cable through where the old one went. You need really sharp cutters to make sure you don't cause the cable strands to fray or it will make it difficult to get it to go through the outer.