You are centering them up correctly and yes that is a good way of doing it.?
Ideally you want tcgt tips, they are designed for finishing non ferrous (aluminium and brass) but they work well in small lathes and will cut steel.
The tcmt tips you have ordered will likely be better than the braised tips but not optimal imo. I won't try and explain why because it's a subject that is quite huge and in depth. But basically its tip geometry, speeds and machine rigidity.?
Unimat Matt