Generally speaking I find HSS more useful and verasatile as you can grind cutting edges, forms etc to suit your requirements,
Carbide tools are more prone to chipping, and difficult to regrind, you need special grade wheels and diamond laps to do them properly.
They also require higher speeds to cut efficiently, and either none or copious amounts of coolant when cutting.
I am not familiar with your make or model of lathe, but generally speaking, any size of tool can be used so long as it is set to cut at centre height, and securely held.