I love linen. It’s more breathable than cotton. The more you wash it, the softer it gets.
If you buy it (In the U.S.), “handkerchief weight” is what you choose for lightweight tops, floaty curtains, and handkerchiefs.
(When the baby is no longer likely to leak, I might invest in linen sheets for us adults, but not for my kids or guests)
I was once in a forum where a woman explained that she bought fabric (you can buy it online for $10-13 yard, last I looked) and made sheets for her whole family. After a year, she cut them down to make bath sheets. (Linen is very absorbent) Then, after a year or so of getting washed and dried vigorously, she made very soft undershirts for her family.
To tell if fabric is real linen, you cut off a small sample and set it on fire. (Really!) If it smells like burning plant matter, it’s linen. If it melts or smells like plastic, it isn’t linen.