A cotton rug is the thing underfoot that softens a room without making a big statement about it. It takes the edge off hard flooring, muffles the sound of chairs scraping and shoes dropping, and gives a space a bit of warmth without the cost or commitment of something wool or hand knotted.
If you own none of these yet, start with a plain weave in a flat color, oatmeal, faded blue, something that already looks a little worn before you've even spilled anything on it. The textured waffle weaves and the ones with fringe and tassels are lovely, but they show dirt differently and they are not the one to learn on. A flat woven cotton rug in a four by six or five by seven size will sit under a coffee table or by a bed without fighting the furniture around it, and it washes easily, which matters more than people expect until the first incident involving a toddler, a dog, or a glass of red that didn't make it to the coaster. These rugs sit well with wood floors, with simple furniture that doesn't need a rug to carry the whole room, and with layering, a lot of people put a cotton rug over a bigger jute one for extra softness underfoot, which sounds fussy until you feel how much nicer that combination is on a cold morning. The small details worth checking before you buy, or the day it turns up, are the edges and the backing. Run a hand along the hem and make sure it is sewn flat, not just folded and glued, because that is the seam that starts to fray within a year if it is cheaply finished. Check whether there is any rubber or latex backing, some cotton rugs have a thin grip layer, and if yours is going on a hard floor without one, you will want a rug pad or it will slide every time someone walks across it fast. Over time, cotton softens. It gets a little looser, a little more relaxed looking, almost like a well washed shirt, and that is part of the appeal rather than a flaw. It will fade slightly with sun and washing, so expect the color after a year to be a touch gentler than the one you bought. Wash it cold, hang it to dry rather than tumble drying on high heat, which can shrink it more than you'd like, and shake it out often since cotton holds dust more than you'd think for something so thin.
I would put the first one down in the kitchen, right where you stand doing dishes, because that is where bare feet notice a soft floor the most.