I am going to redesign a marketing web application for internal use in a big company. The application consists of monitoring different values and KPI's of the company. They have been using it for a long time, but now they want to add new functionalities and redesign it. The Marketing team that is using this web application is composed of about 20 people. Should I first research for Personas?
Yes, definitely research before you start. I would recommend you to do shadowing as well to see how they use the current application and where you can see problems and potential to make it better with the redesign.
Personas are nice to have but personas alone aren't meaningful enough, thats why i would combine other research techniques (like shadowing) so you get more out of your research while investing the same amount of time (you can create personas with the data you gather while shadowing for example).
Personas AND use cases both need to be covered. I would also advise to actually meet with the users of the current design and feature set, get some info what they like/dislike about it, throw some mockups after you have gathered some ideas how to improve things and then using some paper prototypes go to those users again and see how they feel about it. Especially since this is for internal use only and you don't have to cover a large amount of potential users (which would have been the case if the application was to be released on the market) this should not be that difficult to accomplish. 20 people is a very small group of people.
Although I'm not into marketing I'm almost certain that there are plenty of marketing web applications out there that offer some if not even all of the features you are likely to be designing for the new version of this one. Don't feel ashamed to look at those and take some ideas and designs. Remember though: steal like an artist so don't just go copying it all without any significant input of your own. ;)