Most likely the whole branchial basket.
Purpose decides technique.
In this case, I would prefer to take the hyoids, including branchiostegals and interhyal to have a more complete packet of lower head contents. No need to cut anything else. Sometimes you can just pull the whole thing out. There is never any need to remove operculars, just lift up the gill cover, and maybe cut through the branchiostegal membrane. Dissection of cleared and stained specimens in glycerol is better performed with micro-dissection scissors and needles, and you can see better what you are cutting through.