Are there certain kinds of salts that work best for baking (cakes, bread, etc)?
Salt that is used for food consumption is always meant to be sodium chloride (and may or may not contain other things such as iodine). Other "salts" (to use the term in the chemistry sense) such as potassium chloride are not generally used by themselves for human consumption or specified in food preparation, even though they are potentially safe to eat.

Sea salt is still 85% sodium chloride but because it has additional chemicals/elements/compounds in it, does have a different taste.

For best results when baking, use plain table salt, sodium chloride, with or without iodine (which is added to provide a necessary nutrient for those not living near a salt-water source of fish or not eating enough salt-water fish). Note from the link that sea salt does not contain enough iodine to supply a nutritionally adequate amount.