This is, again, where your layers come in – a nice heavy leather for slash damage, a dense silk for piercing. You probably want to put something under it though, silk against sweaty skin is unpleasantly sticky. It *clings*. Eww.
This is where linen, hemp or even nettle (no, it doesn’t sting) comes as the next-to-skin layer; comfortable, hard-wearing, easily washed and not even unusual: “linens” was period-speak for “underclothes” for centuries.
All three are made the same way, more or less, involving a technical vocabulary of retting, beetling, scutching, hackling etc.; look it up.
* The wooden scutching-knife may be and IMO almost certainly is an ancestor of the “Dussack”, a German / Central European training weapon (the real thing would have been a Messer, a large fighting knife). Compare this illustration from a fight manual ca.1570…
…to a couple of modern repro dussacks…
…and finally to a couple of painted antique scutching-knives from Sweden, one marked 1918, so the shape hadn’t changed much in 300 years….
Any fabric where the washing instructions are “boil until clean” will be OK as bottom-layer armour. That’s how its laundry labels say to treat top-quality Irish damask linens inherited from my Mum, so fabrics like hemp or nettle certainly won’t come to harm.
Your characters may interpret it this way: those who boil their under-tunics the night before combat seem to drive off a lot of infection demons and make wizard healing a bit easier.
Finally, a memorable side-note that has literally nothing to do with fabric armour or indeed fabric of any kind: in 1806 (or ‘08) MP and ex-military surgeon Humphrey Howarth was challenged to a duel.
That morning he washed thoroughly all over, then proceeded to the duelling ground in his coach - stark naked, knowing from his experiences as a military surgeon that cloth fragments forced into a wound were the primary cause of fatal infection.
Whether from embarrassment or because it was now A Silly Thing, his opponent Lord Barrymore called the duel off…