Most people buy a side table the same way they buy a phone case, whatever's closest to the checkout, without ever measuring the gap next to the sofa first. Then it's either too short and your coffee mug is basically on the floor, or too tall and it blocks the armrest, and you spend a year walking around it before admitting it was wrong from day one.
Stick with light wood tones, white, or a soft black before you reach for anything glossy or heavily patterned, because a side table is small enough that a bold finish reads as a decision you have to defend forever, while a plain one just sits there being useful. A round one in a warm wood tone sits next to almost anything, a worn leather chair, a linen sofa, even a mismatched armchair you inherited and haven't committed to loving yet. Pair it with a lamp that actually puts out enough light to read by, not just ambiance, and suddenly that corner of the room has a job. If you own nothing else, start with a simple round or square table at roughly the same height as your sofa or chair arm, somewhere in the eighteen to twenty four inch range, because that's the height where a drink or a book feels within reach instead of a reach. Skip anything with a shelf underneath unless you actually need the storage, extra surfaces just become places where mail goes to die.
When you're shopping in person, or the day it shows up at your door, check three things before you let yourself get attached to it. Put a glass of water on it and see if it wobbles, a lot of cheap tables have one leg very slightly off and you won't notice until your coffee is on the rug. Check the actual tabletop width against what you plan to put on it, a lamp and a coaster and a phone take up more room than people expect, and an eleven inch tabletop sounds fine until you try to fit all three. And look at the underside for how the legs attach, screwed into a solid center block holds up a lot longer than legs that just clip onto a thin board, especially if you're going to bump it with your knee for the next five years, which you will.
Living room, next to the chair you actually sit in every night, is where I'd put the first one.