I understand the struggle. Traditionally, I've opted for lower priced options in summer tops for my casual at-home wardrobe. Except for items I plan to wear for going out, going to the city, etc.
One of the best summer tops I own is one I bought 4 summers ago at The Loft, and yes, it is still going strong. It's made of extremely lightweight cotton voile, almost transparent, but the pattern disguises that and I don't wear a cami with it. It's cotton but rarely needs ironing if I air dry it, since it is so light. (Occasionally I do pass an iron over it.) It goes with everything. It has sleeves so feels covered but is so light it's like wearing sleeveless.
I would not neglect a look at the Loft. Most of their stuff isn't great quality, but occasionally you find a real winner. What they have in stock now doesn't look as if it will meet your needs (wrong fabrics and styles) but in another month you might have luck there as the cottons and linens come to the fore.