Step 1: Wash the banana peppers thoroughly and slice them into 1/4-inch rings, discarding the stems.
Step 2: In a large stainless steel pot, combine the white vinegar, water, pickling salt, and sugar. Bring to a boil over medium-high heat, stirring until the solids are dissolved.
Step 3: Place one garlic clove, 1/2 teaspoon of mustard seeds, and 1/4 teaspoon of celery seeds into each of the four sterilized pint jars.
Step 4: Pack the sliced pepper rings tightly into the jars, leaving about 1/2 inch of space at the top.
Step 5: Carefully pour the hot brine over the peppers in each jar, maintaining the 1/2 inch headspace. Remove air bubbles by running a thin spatula along the inside of the jars.
Step 6: Wipe the rims of the jars with a clean, damp cloth. Center the lids and screw on the bands until finger-tight.
Step 7: For refrigerator pickles, let the jars cool to room temperature and then store in the fridge for at least 24 hours before eating. For shelf-stable pickles, process in a boiling water bath for 10 minutes.