There's a point in September, when the big beach bag gets put away and the heavy winter coat comes out, when a shoulder bag suddenly becomes the only bag that makes sense. You need both hands free for umbrellas and coffee cups and whatever you're carrying up three flights of stairs, and a bag that sits on your shoulder and stays there, over a coat, without sliding down to your elbow every ten steps, earns its spot fast.
Stick to shades you won't get tired of looking at. Black and a mid brown go with nearly everything you own already, but a soft tan is the one I'd actually push for, because it lifts navy, grey, denim and black without looking like it's trying too hard. Avoid anything with a shiny patent finish unless you enjoy seeing every scuff under office lighting, a matte or slightly grained leather hides the small knocks a bag takes just from existing in your life. On the pairing side, this is the bag that goes under a plain coat with jeans on a normal Tuesday, then switches to a dress and ankle boots for something after work without you having to change bags, which is the whole point of owning one in the first place.
Here's where the gap between cheap and good really shows itself. A budget shoulder bag looks fine in the mirror for about six weeks, then the strap stitching starts pulling, the corners go soft and start to crack, and the zip catches on the lining every time you're in a rush. A properly made one does the opposite, it softens in a way that actually suits it, the leather relaxing at the edges rather than splitting, and it still closes properly after a winter of being shoved into on buses. Wipe it down when it's dusty, keep it away from direct heat when it's wet rather than drying it on a radiator, and stuff it with something when you're not using it so it doesn't collapse in on itself in the cupboard. Treated like that, a decent one will outlast several cheaper ones bought to replace each other.
If you've got none of these, start with a mid sized one in tan or black, structured enough to hold its shape with a strap long enough to sit comfortably over a coat, not just a jumper. Avoid anything that only works crossbody, you want the option of both.
Tomorrow morning I'd have it over a plain coat, with jeans, trainers and nothing else to think about.