1st step is to drill a depth hole ~ 1/4”-3/8” with hand held drill bit. If end grain, makes it easy to start the tool in the center, x-grain it makes it easy to end the cut, and of course its an indicator of where to stop to check bottom t.
Generally I’ll start hollowing with a 1/2” spindle gouge. When it starts to squeal or chatter due to length off the tool rest, I’ll start using shop made hollowing tools or a scraper.
I have several bar shapes that use an 8.9mm flat top round carbide insert, 1/2” bar with a 24” handle. I also have another with a 5/8” straight bar with a 10mm cupped carbide insert, mounted parallel with the bar - its a copy of a Hunter tool. It is more catchy vs the flat tops but leaves a better finish. I’m getting to know this tool better with time. The biggest issue is me - I get greedy and let it take too big of a bite.
For shallow boxes, say ~2-1/2”, I may just use scrapers. The deeper the box the more likely I’ll use a hollowing tool. Chatter tells me which tool.
I’ll usually use neg rake scrapers to get the final surface finish. I make quite a few potpourri “boxes” with undercut rims, and the cupped carbide tool is very good for the undercut.
I prefer curved corners for boxes. If you like square corners, flat end scrapers, thick enough to handle the depth, are the way to go.