The one thing worth knowing before you hang a single painting is that scale matters more than subject. A small painting on a big wall doesn't look charming, it looks lost, like a postage stamp on a barn door. Measure the wall first, then go looking for the art, not the other way around.
If you own nothing yet, start with one larger piece over the place you actually sit, the sofa or the bed, rather than a cluster of little ones scattered everywhere. A single painting that fills most of the width above a sofa does more for a room than five small ones hung with great care and a level. You can build out to a grouping later once you know how you like to live with color on the wall, but the first purchase should be the one that anchors the room when you walk in tired and just want it to feel finished.
What separates a painting that holds up from one that starts looking sad after a year usually comes down to what's underneath the paint. A canvas stretched tight over a real wood frame, with corners that don't wobble when you knock on them, will stay flat for years. Cheaper ones use thin frames that warp with humidity, and you'll notice the canvas start to sag in the middle like a trampoline nobody wants to jump on anymore. Run a hand along the edge, it should feel solid, not hollow and papery. The paint itself should have some texture to it if it's meant to look like a real brushstroke, not a flat printed sheen that looks fine from across the room and a little sad up close. Touch matters here, a painting with actual texture catches the light differently throughout the day, which is half of why it feels alive instead of decorative.
On color, the ones that are easiest to live with over time are the ones with a muted, slightly dusty palette, warm neutrals, soft blues, faded greens, rather than anything bright and saturated that matches a cushion you'll eventually replace. Abstract paintings in tones close to your wall color blend in and let other things in the room do the talking, while a painting with one strong contrasting color becomes the thing everyone's eye goes to first, which is worth deciding on purpose rather than by accident. Black and white or sepia toned pieces are nearly impossible to get wrong, they sit quietly in almost any room without demanding you redecorate around them.
The real mistake is buying art to match a cushion or a rug instead of buying something you'd still want on the wall after you've replaced that cushion twice.