The one I reach for is the morning I can't decide what I'm doing with my day, meeting at ten, something more scruffy by three, and a plain or graphic tee under a shirt or cardigan means I don't have to decide at all. It's the first thing in the drawer for a reason. School run, desk day, train somewhere, it covers all of it without me having to think past half seven.
The main thing a good t shirt clashes with is a bra doing the wrong job underneath it. Thin cotton shows every seam and every bit of texture, so a heavily textured or very structured bra will print straight through, and anything with a bow or a diamante bit in the middle will announce itself to the whole office. Keep the lines under it as plain as the shirt itself. Past that, I'd steer clear of pairing a big graphic print with anything else busy, you end up looking like two outfits had an argument and both lost.
Fit is where most of these go wrong, and it's rarely the size on the label, it's the shoulder seam. If it sits halfway down your upper arm instead of right at the bone, the whole thing hangs wrong no matter what size you sized up or down to. Cropped ones need checking sitting down as well as standing, because a length that looks fine in the mirror can ride up to properly undignified once you're bent over a desk. And always check the neckline on a cotton one before you wash it once, because that's the part that stretches and goes baggy first, especially on anything with a wide round neck rather than a proper rib.
How it ages depends almost entirely on the fabric weight. A thin, loose weave one will go see through and slightly bobbly within a few months of normal washing, no matter how careful you are. A heavier cotton, the sort that feels like it has some body to it when you scrunch it in your hand in the shop, holds its shape for a lot longer and doesn't go thin at the shoulders first. Turn them inside out before washing, keep them out of the tumble dryer if the print matters to you, and in the shop, pull gently at the hem and the neck rib. If it springs back straight away, it'll survive you. If it stays stretched, it'll be out of shape within a fortnight.
Worn under the blazer I never get rid of, it stops the whole thing looking like I'm trying too hard for a Tuesday.