There are visa for all Schengen states and specific visa for only one or a few of them, but such restricted visa are unusual.
Schengen visa may be single or multiple entry. Getting just a single entry would be typical for first-time applications.
Schengen visa have both a duration (maximum number of days in Schengen) and validity period (earliest and latest date to use the visa). Getting just the number of days you have asked for would be typical for first-time applications.
Last but not least, you must not misrepresent your travel plans in your application. It sounds as if you plan to do that.