I have a Behringer DJX700, and I want to send the master signal to my laptop. Do I need a sound card for that? Cant I connect it to the microphone input of the laptop using an RCA-to-minijack cable?
The Behringer DJX700 specifies for line signals a SNR of >80dB and >70dB of cross talk separation. Against all the "ultra-low noise" and "professional" and "studio" verbiage, that is unexpectedly blunt.
At the same time, laptop microphone inputs are a notoriously bad match to line outputs and of low quality, so you are likely to get pretty bad results.
Most soundcards will be overkill for that purpose. You might consider some "USB soundcard" with 3.5mm line input that is about the size of a cigarette case and with a $20 price point. Admittedly their frequency response will tend to drop off after 15kHz or so, so they will also affect sound quality even with this setup, but the DSP in your mixer only uses a sample frequency of 46.875kHz and thus will not produce much more, even though the analog part of the mixer is specified up to 55kHz. You'd use the "tape out" RCA to connect to the 3.5mm line input of the "sound card".
A "proper" setup would use the "Main Out" balanced outputs of a mixer to balanced inputs of a proper soundcard (balanced line inputs tend to be 6.3mm TRS sockets). Unbalanced connections and RCA plugs aren't really used with professional gear, and the >80dB SNR level of the Behringer mixer will easily be >105dB or more with good analog equipment.
As long as the mixer you have meets your demands, a mini soundcard with stereo line inputs should be a reasonable combination with what you have. Once you want more, there may be a point in looking for a mixer with built-in USB interface.
High quality recording is done using multitracking instead of recording the live mix. For mixers with built-in USB interfaces, you want to check that they are indeed providing all channels separately. For some reason, that was a lot more common with Firewire-equipped gear when that was still a serious option.