Well it depends
To start pretty much all of the finishes sold nowadays are food safe once cured.
Vegetable oil depends on the type of vegetable, some are a bit apt to go rancid and many don't provide a whole lot of protection. Walnut oil is pretty inoffensive except to people with nut allergies, they don't like it that much for obvious reasons
I've used linseed and tung successfully as well. Beeswax by itself doesn't imho provide a lot of protection, its certainly foodsafe but it isn't super hard or resistant to use. A Carnuba wax blend is a bit tougher but still will get rubbed off in heavy use.
Tung is somewhat more water resistant than most other oils, I did a bunch of taster trays that see hard use in a brewpub and finished them with waterlox which is a tung oil based phenolic and they've stood up real well to a wet and rough environment. Some of the other oils like hardware store "boiled" linseed oil have metalic driers that some folks find objectionable, personally I don't see them as a real concern but you can certainly make up your own mind.
I know others here use wipe on poly or similar finishes, they have their ups and downs as well, but are pretty cost effective, easy to apply and survive fairly well in normal use.
For some pieces I use WoodTurners Finish, which is a water/oil urethane mix. It has a (possible) advantage of drying really clear and not coloring the wood much at all. Sometimes this is nice, other times.. not so much.
Different companies "salad bowl finishes" can vary wildly in formulation, one way to figure out just what the heck is in them is to look at the MSDS. For instance here is the MSDS for Behlens
http://www.behlen.co.uk/safety/B603-00014.pdf from which we can deduce that the active ingredients are at least ~10% tung oil in a 40-50% Toluene/Naptha delivery agent and a cobalt drier and about 40% alkyd resin. The alkyd resin provides most of the structure and the Tung oil provides some water resistance. It doesn't tell us what kind of alkyd resin it is (long/short) or what the source oil for that was (probably soya or similar, but mostly functionally irrelevant). A phenolic resin would be slightly tougher, but may not matter a lot in the grand scheme of things.
So what the heck does that mean?
Decorative or low wear bowls I'll just do with a quick oil + wax coating. You have to reapply it every so often but it looks pretty decent out of the box and it quick and easy. Straight beeswax, while perhaps traditional, isn't as durable as a harder wax like a carnuba base (I use mostly Johnsons Paste because its available locally).
For high wear bowls I want a film building finish. I think a phenolic resin+drying oil like waterlox is probably one of the tougher things you can easily put on with minimal equipment, although alkyd resin+oil like the Behlens isn't going to be a lot further behind. Poly is decent and I wouldn't say no, but I've had some more problems with it on other projects if they have a lot of water exposure where the poly will "blush" (turn white), but other seem to have good luck so ymmv.
Finally there are a bunch of other options like lacquer (which makes pretty shiny) or urethane (i.e. woodturners finish - but there are definitely other cheaper options I've been to lazy to explore) which definitely have a place for getting a specific look.
I'm sure there are others or I'm misrepresenting some so don't throw stone to hard please
As to a favorite, if you asked three turners which was their favorite I'd bet a doughnut you'd get four different answers.