I know I,ve said this before,but I dont think you can go too far wrong by buying a few pieces of HSS and grinding your own toolbits. Many people do it,it,s cheap,good training,and if you break a tool,so what ? you just regrind it !
Just to show how simple it is,even I can do it,and that,s saying something ! I seldom if ever use tipped tools or indeed buy in ready made turning tools,it,s much more fun making your own.
Having said that,when I first bought my lathe,I bought a cheap set of tools with it,five -in-a-pack type. Nothing wrong with them,still use them from time to time,then I got stingy and began grinding my own,turning,facing,threading,boring,ect. It,s no big deal,and you learn a lot along the way,so give it a try.
HSS is cheap enough and a little goes a long way,when you learn how to make holders for those little bits !!
Give it a go !!