Just use integers, and fields ending with "_cents".
There is no ambiguity, rounding problems are not even an issue, serialization and deserialization will pose no problem when dealing with external actors, and you can still sum money easily in your db requests.
Problems will arise when you'll do multiplicative operations on money, for instance when working out taxes. There are precise rounding rules to apply, and the solution is to tackle these issue one abstraction layer above, on the operations rather than the values, because some time you'll want to carry out rounding between each tax operation, sometimes at the end, on one line or on a whole batch of transactions.
Other problems you'll bump into is the asynchronous nature of money flows. You won't realize it with credit cards (well you'll figure it out soon enough when you'll stumble upon "race conditions"), but this becomes explicit when dealing with mandates, direct bank transfers or checks. You need to move the money out of sight of the user in a ledger specific to that person that holds transactions being processed (can takes days or weeks in some case) and move it back to the original ledger if the transaction fail. Otherwise you'll bump into issues of double spending. This is something that is out of your control sometimes (had the unfortunate experience to issue withdrawals multiple times on a big bank's payment processor API and theses dunces sent the money multiples times). Use idempotency keys profusely as well as (distributed) locks. The hardest part is not getting your part right, it's handling external actors bad implementations. Also fuck HTTP w/ hooks. Some actors do not even make sure you received the webhook. The non binary aspect of HTTP is a bullshit argument and I'd gladly trade it for a binary protocol that has strong quality of service mike MQTT, since anyway I'll have to implement some kind of smart broker when issuing orders to a shitty HTTP api anyway.