I've been working with these a while. I picked up a pair of X540-T2 - they're 'server' cards, so run a little hot, though there's a version with a fan. The T suffix means native copper support so you don't need a SFP.
They're PCIe 2.1 x8 for TWO ports, and you can run a single port at full speed (tested by speed test) on a x4 slot with no issue. The x550 is a newer version that'll work on x4, but I've not found them cheap on the secondary market. They're about 90usd + shipping on aliexpress, but prices vary wildly. They are EOL but the current intel drivers support them. They won't downgrade to 2.5 or 5 gbps, so you'll need a 10gig copper capable switch or connect them directly. On windows the drivers are excellent and easy to use, and as older cards they're well understood. They have a mild tendancy to overheat, so run it on a system that's capable of cooling it. While both these cards are "obsolete", they're common and supported with current drivers.
I've not tried it yet, but most modern low cost 10Gbps cards are based off Aquantia chips - they'll work with the 'slower' multigigabit standards and are about the same price as my x540 for a single port. They do PCIe x4 and seem a better option in quite a few ways. I believe asus sells one, as well as various chinese vendors like comfast.