Any fans will normally work. It is true that the fan thickness also matters, and there are a few out there that have single sided brackets (so they can only be mounted in one direction), but you are normally pretty safe with 120mm fans. Normal 120mm fans are 25mm thick.
Keep in mind that using a site that shows pictures is best, as the power plugs on fans do vary. There are three normal types of power plugs on fans, Molex (the big connector that doesn't report fan speed), standard 3 pin (power, ground, and rpm), and 4 pin PWM fans.
Good luck!