Always start with a RUQ sono. If sonogram is equivocal but there is clinical concern for cholecystitis, then can obtain a HIDA scan. A HIDA also helps with cases of acalculus cholecystitis (no stone on sono, but no filling on HIDA) and chronic cholecystitis (where it demonstrates decreased ejection fraction).
CT scans are not really done on purpose for GB pathology. If there is need to look at the pancreas or liver, then CT with contrast is the way to go.
If there is evidence of choledocolithiasis (a stone in the CBD) or gallstone pancreatitis, then ERCP is helpful because it can both find the stone and remove it (usually prior to cholecystectomy) to relieve the obstruction. The test question concerning ERCP will often center over the risk of post-procedure pancreatitis. A non-invasive way to assess the biliary system for stones prior to ERCP is with MRCP (a special MRI sequence)