If you do live recording of a band, you can save time and space using a mixer with USB. For less than $100 (actually just above the cost of OP's current mixer's used value.) In the < $150 price range, the unit will likely be limited to 44.1/16 but that is not a critical loss because the digital path will be cleaner and quieter than the audio path through the PC 1/8" soundcard. All of the major manufacturers have good quality option and similar features. Here is an example for a Behringer unit -
Behringer Xenyx q1202usb Mixer To get the best quality transfer using your current mixer, you should get a two channel input/output audio interface such as the Behringer U-phoria UMC202HD for $79 or equivalent. This Beringer is the most cost effective solution that provides good preamps and converters.
Behringer U-phoria 202HD If you record your band or yourself live, by far, the simplest, best and most convenient and rock solid set up is to use a Stand alone multitrack digital recorder. Zoom, Roland and Tascam offer a variety of models so you should take care in choosing the right one for your needs. It is worth the cost difference to bypass the two,four and six input units for one of the 8 input models such as the Z00m R16, R24 series or my personal recommendation is the Tascam DP-24. It is designed specifically for recording a band live and offers features none of the other brands unit do in regard to live recording. Behringer also offers a series of Stagebox PA systems that do not have any buttons, knobs or controls but are controlled by ethernet or wifi from an Ipad/Android tablet. These units can record a stereo recording on a flash drive as well as having usb audio interface capabilities. The XR18 is the only unit that has more than 2x2 recording with the capability of 18/18 usb in and out. Many of the new mixers with usb also have direct stereo recording to an SD card built in.
You have a lot of choices for multi track recording today.