Most PC power supplies will require some load on the 5v rail in order to get a decent current draw from the rest of the rails. In other words you may need to load the 5v rail with a resistor or a light in the order of about 10W. 5V or even 3.3v rails are the regualted rails. Open the box and see which one has the feed back. that will tell you which rail to load
This only applies nowadays to cheap 10-30$ power supplies, which are based on old designs. Yes, on those power supplies there has to be something connected to the 5v output so that 12v output will be stable. These types of power supplies already have resistors connected inside on the 3.3v and 5v and 12v to provide the smallest amount of load (usually 1-1.5 watts) to keep the power supply from oscillating or go way out of atx specs but in some cases an additional load on the main rail (usually the 5v one) is required.
From 40$ and up, you can get power supplies from brand names that are based on modern designs and manage to regulate 12v and 5v properly, no matter what so extra load is not really required.
Anyway... light strips are made out of leds... and leds are current driven, not by voltage. LEDs have a forward voltage and once you reach that, they'll light up and the brightness will vary depending on how much current you push through them.
In a led strip, they may be connected usually in two ways...
One way, a few in series to get the 12v divided to 4-6 leds and get the voltage drop on each led around the led's forward voltage without caring about the current, then all these series are in parallel connected to 12v
Second way, series of sets of leds, where each set has its own constant current regulator which gives a constant current to the leds no matter the voltage.
So in both cases, the led strip won't care that you don't have quite 12v on the output and won't care about the ripple
A linear adjustable power supply will usually have under 10mV ripple on the output, actually should have 1-2mV ripple or somewhere around that value. So the output voltage is much cleaner. In addition, a linear power supply will have a method to limit the current to a certain value, an ATX power supply won't, it can output all its power if there's a short.
An ATX power supply only has to have the ripple under a certain value specified in the standard...for 12v the value is about 120mV, for 5v is about 50mV... most no-name cheapo power supplies don't respect that and at low loads such as a microcontroller and a lcd screen and some leds the ripple can be much higher.
Also due to design of the power supply, which switches 50-80k times a second, the output fluctuates so many times a second, it's a noisy output.
Some microcontrollers or chips are sensitive to such high ripple values so you can get erratic behavior in a circuit and pull your hair out unable to determine what's wrong.
Now you could still use an atx power supply to power your circuits but I'd recommend at least taking the 12v and moving it through a linear regulator such as a 7805 chip to get 5v with a lot of that noise removed... or use a low drop regulator such as *1117 (lm1117, amc1117, nxp1117, it's jellybean components, lots of manufacturers make it) to get 3.3-3.6v out of the 5v rail (3.6v is a value often used on microcontrollers)
If you're paranoid you can also make a pi filter on the output to smooth it out even more (an inductor between two capacitors) or even ferrite beads at the input and output of the linear regulator