Yes, those LED strips can be power-hungry. They also benefit from being fed power from both ends if you're running more than a metre or so, but if you're hacking them up into 7-segment figures, then that's less of a problem.
Main gotcha is if you can't mount the power supply close to the LEDs - at high currents the voltage drop on the cable run can be significant, and the LED drivers don't like their power supply dropping out. The proper way to solve this is with a PSU that has a remote sense input.
Flap displays are lovely, but unless you happen to dumpster-dive a suitable one, expensive.
LED matrix displays are another off-the-shelf option, but they often aren't particularly elegant about how they refresh on receiving external data. I wouldn't want to do a seconds countdown on one unless I could make the display controller do the updates itself. Minutes would be fine.