For crispest pickles, slice off and discard the blossom end of the cucumber. It contains enzyme that can make pickles softer.
For best results, use pickling cucumbers, which have less moisture and fewer seeds than conventional slicing cucumbers. These are often available year-round in the produce section of larger grocery stores and are abundant at farm markets (and backyard gardens!) in the summertime.
Don’t have a canning jar? You can use another large container. Ceramic or glass work well. Avoid plastic or metal.
Don’t have a jalapeño or another variety of fresh hot pepper? For a backup, you may use red pepper flakes. Plan on ¾ teaspoon to provide heat similar to one jalapeño pepper.
Can you use a different vinegar? I have tried this recipe with apple cider and red wine vinegar. Though the resulting pickles aren’t bad, I do prefer the more neutral flavor of basic white vinegar stipulated in the recipe by a wide margin. A white wine vinegar may be a better sub, and in a pinch, apple cider vinegar would be my choice over red wine vinegar.