How many agendas of each type of agenda can be scored? It is possible that only one of each type can be scored and the corporation wins the game with 7 agenda points total.
Agendas typically follow the same rules for deck composition as any other card in Netrunner. This means there is a maximum of three copies of the same card allowed in a deck. Either player can score multiple copies of an agenda, especially if the reward for scoring it aids their playstyle (e.g., using Priority Requisition to rez big ice in a glacial build, or Astroscript Pilot Program in a fast advance deck).
There are a couple exceptions to this rule, but they will say specifically on the card that only one can be included in a deck (the most recent card like this is Jinteki's Philotic Engagement).
If you are playing core only, you should take all of the faction specific agenda AND all of the neutral agendas for your deck. This will mean three copies of Priority Requisition, and Private Security Force, plus the in faction ones. In a typical built deck (49 cards), you will need 20 agenda points to be in the deck, made up however you want from the available neutral and in faction agendas.
Agenda types are not restrictions on scoring. If they were, the starter Jinteki deck would not be able to win as it contains 6 Security agendas and 3 Initiative Agendas, none of which are over three points.
Agenda types are presumably there to allow future cards to interact with them. As of the Lunar Cycle, they are still unused.