For most of the BPO you don't need any skills to research them, except Laboratory Operation for more slots.
However, some more advanced BPO require you to have certain skills, as listed below:
- Research
- Metallurgy
- Electronic Engineering
- Graviton Physics
- Armor Rigging
- Shield Rigging
- Projectile Weapon Rigging
- Launcher Rigging
- Drones Rigging
- Hybrid Weapon Rigging
- Energy Weapon Rigging
- Astronautic Rigging
- Electronics Superiority Rigging
- Energy Grid Rigging
- Mechanical Engineering
- Jury Rigging
- Amarrian Starship Engineering
- Gallentean Starship Engineering
- Caldari Starship Engineering
- Minmatar Starship Engineering
- Rocket Science
Additionally, for T2 BPO:
- Quantum Physics
- Molecular Engineering
- Electromagnetic Physics
- Mechanical Engineering
- Nuclear Physics
- Laser Physics
- Hydromagnetic Physics
- Nanite Engineering
- High Energy Physics
- Graviton Physics
I don't believe you own a T2 BPO, but in case you get your hands on one.
All those skills require different levels for different BPO, but I suggest to use EveMon to look at what level unlocks, so you will know of you gonna need it or not.
I did not take faction items into account. You CAN research them before manufacturing it, but you can only get BPC at the LP Stores anyway.