You can solve this problem easily. Take a plastic record sleeve and cut it to the size of the record. Punch a hole in the middle of it for the spindle and insert it under the slip mat. The current market leaders today are Stanton and Ortofon , both of which make excellent Cartridges. Ortofon does not offer as wide of a variety in affordable cartridges, but delivers an oustanding product.
Needles endure much abuse and are replaced quite often.
For obvious reasons the more you spend the better the performance, but for home use, the lower end models are sufficient. All mixers are comprised of the same basic parts. Certain criteria must be met though, as some have more options than others. A inch headphone socket assignable to both channels. It may be in your interest to have more than two channels if you wish to add input of other audio sources such as a CD player, FX, Sampler, Drum machine or Microphone.