I have to attend a business meeting in Spain for 5 days and after that I plan to have a trip in Europe with my wife, she will arrive after I complete my business meeting. Shall I apply for visa the separately - business and tourism visa for me, and tourism visa for her? Are there any implications doing this?
Generally, the categorization of Schengen visas is not particularly strict, although you do have to select a "main purpose of the journey" on the application form. The form is given in Annex I of the Schengen Visa Code.
In your case, this will be "business," and in your wife's case it will be "tourism."
Shall I apply for visa the separately...?
You have to submit two application forms in any case, even if the purpose of the journey is the same, because the application form does not support multiple applicants. You might want to submit your application first, in case your visa is not approved or is limited to just period of your anticipated business travel. This would save your wife from having to apply for a visa for a trip on which you cannot accompany her. But if you don't mind that possibility, you can certainly apply at the same time. If traveling to the application center is burdensome, it might be better to do that and try to get appointments at the same time.