Number of firms to apply to
In terms of numbers - it depends on the type of candidate you are. If you believe you have a reasonably high chance of getting in given your school, GPA, extra curriculars then it is better to be selective. This allows you to spend time networking with the firms you are interested in and truly getting to know the culture and nature of projects you want to apply to. It also sets you up better once you join the firm as you can leverage these relationships to get staffed on interesting projects.
Types of firms to apply to
While you can apply to both consulting and investment banking roles, if you were to interview for both roles at the same time it would be a highly stressful experience. Consulting interviews require a different skillset vs the more technical IB interviews and the limited overlap would require a lot of work on your end to do well in the interviews.
All the best!