or you can try spending output with very high fees so miners will need to confirm first transaction in order to claim high fees from your transaction.
Does this really work, though? I've heard similar claims in the past, but wouldn't the low-fee (or in this case zero) transaction still cause issues? Otherwise we could just send a ton of transactions with zero fees, then spend a bigger one with a small fee (like to condense 10000 small txns, for example).
Yes it works,its called child pays for parent but it works only if average transactions fees is is equal or above current best fees for faster confirmation.