imo, it boils down to personal choice. I have used a Longworth chuck, a vacuum chuck and a donut chuck to secure the vessel and turn the bottom. I pretty much have gone to a donut chuck. For me it is the most secure.
I have used Cole jaws and longworth chuck. I have found the longworth has to be screwed down very tight to feel sure that I won't have a flying bowl. The Cole jaws are better but again don't feel super confident. The donut chuck sounds like the way to go.
I gave upon a Longworth chuck as I didn't trust the grip it had. Without a vacuum pump, My goto is my set of Cole jaws. Also keep the tailstock engaged as long as possible. With a long skinny live center, there won't be much to cleanup with the bowl unsupported.
I use a donut chuck, but keep the tailstock in place with a 60° live center for as long as possible. Then when I'm happy with the bottom, I remove the tailstock and carefully turn off the nub that remains. On a few occasions where the donut chuck wouldn't fit, I've used cole jaws but added lots of masking tape to hold the bowl firmly in place. And, keep the tailstock in place as log as possible.
I have both a vacuum pump and a Longworth chuck. Recently I find myself using the Longworth chuck exclusively. Although the donut chuck holds the piece more securely I haven't had a problem with the bowl coming loose from the Longworth chuck probably because I use light cuts and a fresh EWT cutter. YMMV
Some day I will probably take the time to build a donut chuck and try it.