Don't be tempted to buy bigger diameter tools, (3/4-1") stock, 1/2" max should be adequate.
The important factor is your personal control of the tool, bigger diameter tools, dependant upon the grind tend to take bigger cuts/bigger loads, this needs more robust user control and applies larger load on the work piece.
Concentrate on developing user skills with the 'standard' gouges, move to bigger diameter stuff when you are turning something in the 3-6ft diameter on an appropriate lathe.
As someone relatively new to turning you might get away with using larger tools on a nice green log giving little resistance but the day you pick up the same tool to tackle a piece of dried oak could provide a sharp surprise.
On deep bowls, as smaller tools have a limited stiffness and handle length for control make sure you have tool rests to reach inside the bowl and as near the cutting edge as possible.
If making large diameter flat surface platters a thick stiff straight faced scraper
use can be seen here can be very useful for planing any surface ridges out.