You can get 3 PROJECT Icons with Caches at 750 IP each (2250 total). Each of these will have a Summoner Icon, an Augment Cache Fragment, 2 PROJECT Cores, and the First Strike Blueprint (which unlocks the First Strike border for a Project Skin - Ashe, Katarina, or Ekko). Additional Caches can be bought for RP.
You'll end up having 3 First Strike Blueprints, 6 Cores, and 3 Cache Fragments from these. The 3 Cache Fragments combine to make an Augment Cache, which will have a skin shard and some other loot, and may have another Augment Cache Fragment.
After getting these, get the Disruption Cache for 1500 IP, which will have 7 Cores, a PROJECT: Overdrive Blueprint, and 2 Augment Cache fragments (iirc).
You should have at least 13 Cores total, plus the rest of the loot. Using 7 PROJECT Cores, you can craft the First Strike border for the Ashe, Ekko, or Katarina PROJECT skins if you own the skin. Or, you can use 12 cores to craft a PROJECT: Overdrive (Yasuo, Yi, Zed, Fiora, Lucian, or Leona) skin shard from the Blueprint, which you can then unlock using Hextech Crafting.