FIRST, I always use a surge protected power strip for omputers, DVD players ect, even for My wifes $3000 Embrodry sewing machine (yea I know that cost more than my computer - LOL).
That said, they do next to nothing to protect against a power outage/back on. Surge protectors are designed for High ENERGE spikes normally caused by lighning.
You really need an UPS.
For modern computers, using the power off from the OS does NOT totally shut down the Computer as the PSU will still supply some voltage to the Compter such a the 5 Volts. Myself, When powering off I shut the computer down, then turn the power switch on the strip off (not a requirement if connected to an UP, but is for all the other odds and ends if not powered by an UPS.
For UPS, make sure it has a "near" sinewave ouput, NO a modified sinewave as this modified sinewave can damge some PSUs and other electronic subsystems.
Reason is the Input transformers are designed for a sinewave and do NOT take kindly to the near instant change from a given voltage level to zero volts