Both animal cells and plant have DNA and RNA. To choose either proteinase K, RNAse or DNase, you should determine the purpose of nucleic acid extraction. If you need to extract DNA then you want to get pure DNA, without impurities i.e. protein and RNA. Then, you can use proteinase K and RNAse.
If you need to extract RNA, then you can use proteinase K and DNAse.