Pro-tip, don't buy exotic ammunition that was never actually sold to the general public from dodgy guys on the internet. That youtuber who nearly blew his face off recently with his 50cal wasn't the victim of expired ammunition; his ammunition was almost certainly counterfeit and "handloaded" with the wrong powder or far too much powder.

In old ammunition, the primary concerns are the corrosive residue the ammunition will leave behind, rounds that won't go off at all, or rounds with a delayed reaction ("hangfire".) Hangfires can be dangerous if they go unnoticed, but aren't spontaneous "gun explodes in your face" events. You're also fairly likely to experience hangfires and rounds that simply don't work when shooting new production cheap 22lr; rimfire is notoriously unreliable and when rimfire ammunition is made cheap, you'll encounter 'duds' often enough. If you're at a gun range just trying to have fun, this is generally little more than an annoyance.

Centerfire ammunition is more reliable in general. With ancient centerfire ammunition, you have to wonder whether the ammunition was ever any good in the first place. A century ago, there were plenty of companies/countries making really shitty rifle ammunition that you might still find for sale today. That ammunition was never good at the time, and age hasn't made it any better. But some companies/countries were also making perfectly good ammunition a century ago, and that ammunition is generally just as reliable today as it ever was. But it will leave behind hydrophilic corrosive salts in your gun, so maybe think twice before shooting lots of it then neglecting to clean your gun.