I have a dual credit/debit card (living in Europe). It is basically two different cards in one plastic, up to the point that actually they have different card numbers, even if it is only one physical card. Credit side works as credit cards most often work: It will add the purchased sum to the credit account which is then billed from me afterwards. Debit side takes the money from the account which the card is tied to. Paying method is same for both, as it is chip card it will require the pin code for both sides (or if the merchant is having only outdated equipment, it can be done by swiping the magnetic stripe and signing).
What I would like most is "online" debit card but they are sometimes so durned slow to use that I just use debit. But I get irritated as the transaction does not show immediately on my account and then it's hassle to memorize/hunt receipts to check if all transactions are showing and how much I really have money left.
As around here all places have cart system like your Aldi's have, there are also market for key fobs which have removable coin-sized disc you can use to obtain shopping cart. They are life savers for those who rarely carry coins/cash on them! Flat washers may also work if they are right size, so you can make your own if they do not sell these there.