C2 insert for non ferrous turning, and if you are not flooding or misting, them may be coated inserted if you machine has the need power to get things hot.
C-5's inserts are for ferrous metals.
The downside to a TT insert is that the tip is only so narrow (read rounded), so if you need sharp square inner shoulders or a fine finish cuts, then you want to use a HSS inset for these last cuts instead.
Carbide cutters allow you to remove a lot of metal fast, but do not cut to the same fine finish as a HSS cutter. If you have a lot of rough/deep cutting that you need to do, then carbide insets are the ticket. If all you are working on is finish cuts/sharp type angle cuts in aluminum, then you would want to be using HSS cutters instead. As for HSS inserts, kind of a waste of money unless you are doing production work. Instead, a grinder and HSS blanks are the way to go.
Yes, inserts allow for a quick tip change if you crash, or wear a tip out, but for the price your going to pay in the long run for even HSS inserts and non production use, would save buckets of money by just grinding up a few HSS tools instead. So on that note, yes, you do want a set of index-able cutters for when you need them (such as have to face/set back hardened steel and going to be using carbine tips), but for the most part, chances are you will not be using inserts (even HSS tips) as you main stable for finish cutting due to the over all expense of them.