Prepare canning jars and lids by sterilizing them according to standard canning procedures. Alternatively, ensure jars are very clean for 'refrigerator pickles'.

In a large non-reactive saucepan, combine the water, vinegar, pickling salt, and sugar. Bring the mixture to a rolling boil over high heat, stirring until the salt and sugar are completely dissolved. Remove immediately from heat.

Pack the jars tightly. Divide the garlic cloves, dill heads/fronds, peppercorns, and mustard seeds evenly among the sterilized jars. Pack the cucumbers vertically into the jars, leaving about 1/2 inch of headspace.

Carefully pour the hot brine over the cucumbers in the jars, ensuring all solids are submerged. Tap the jars gently on the counter to release any trapped air bubbles.

Wipe the rims clean, affix the lids, and screw on the bands until fingertip tight. For shelf-stable pickles, process the sealed jars in a boiling water bath for 10 minutes. For refrigerator pickles, allow them to cool completely before refrigerating.

Allow the refrigerator pickles to cure for at least 48 hours before enjoying. Shelf-stable pickles are ready after 2 weeks of cool storage.