In cross sectional studies if you have the complete sampling frame you can use either simple random or systematic sampling method to select samples. Use computer generated random nos, to select. If you have big population to sample you can use systematic random sampling technique. It depends on what is u r sampling unit. If it is field trials you can use cluster sampling method accounting for design effect.
In case control studies if you have more no. of cases (with inclusion and exclusion) you can use simple random or even systematic random sampling method. controls also can be selected similarly people with out the disease condition under study.
For cohort also among people with specific exposure if more use systematic random sampling . Especially in hospital based studies if the estimated exposed peoples are more systematic sampling will be ideal
Thank you so much. Can we also do blood test ,along with observations ,to find out exposure ,in patients with disease, in case control or cross sectional studies ? If not then what type of study design it would be if we do blood investigation?