I'd wait for the next T-series models to come out, if the replacement isn't urgent. Really curious what Lenovo is going to do with them. Although the new Skylake models will all lack VGA and require an adapter (not just a dongle, but a full exterior DAC.)

That said, all 3 meet your needs, but:
X250 - much smaller, personally I can't live with a 12" screen as my primary machine. If you can live with the smaller screen, maybe the best option?

X1 Carbon - dongles, and SSD mini-card only (and not sure how easy it is to access and swap.) Really nice design, and absolutely tiny for the screen size. Just enough pricier that if it were my own money (or maybe even my own budget out of my employer's money), I'd look at cheaper options (especially with a lower-end 8gb config) but if it's a standard machine at your employer I doubt they're tracking the difference.

T450s - real ports, still reasonably thin/light, not a tiny screen. Probably the best compromise given your comments

Is swapping the HDD include SSD mini cards? Not sure how accessible the HDD or SSD is on any of these; Lenovo used to make these things really easy to access, but the last machines I played with in that sense were the T430s/W530 generation.

If it's your own money, or your employer also gets Dell, have a look at the Latitude E7450. It's just a hair chunkier than the T450s, but it's got a somewhat more standard keyboard and it is an absolute joy to open up and work inside, and still has a full set of ports.