There is a range of serial numbers to avoid below a certain number where the receivers were improperly heat treated and can be more brittle. It’s a well known thing you’ll easily find online.
Other than that exception, modern ammo is fine.
They had a pristine 03 in the local gun/pawn shop a few years back and it was reasonable priced and I was about to purchase it and ran the serial numbers. They ran in the range of the brittle receivers. I was dejected and passed.
I did manage to snag a really nice one made in 1931 from CMP that is a great shooter and an Enfield 1917 as well before they sold out of both. About your best bet now is a pawn shop and then you just have to get lucky and you will pay if the shop knows what it has.