Hopefully Constantine will come along with a better list!
Industry
Production Efficiency
Mass Production
Advanced Mass Production
Supply Chain Management (Can build from a region away then!)
*Racial Starship Engineering
*Racial Encryption Methods
Theres various other skills relating to capital ships and T2 ships too, but I think this is it for now?
Industry of at least III (reduces manufacturing time and allows learning of Efficiency) eventually to be trained to V , miners will have it at V anyways as its required for barges.
Production Efficiency is THE MOST important skill, reduces wastage of minerals, at V its 20% less usage of materials. needs industry III ( if you have it at 3 cut your teeth in the ammo business , loss is small compared to ships where1 point in efficiency can easily be a few Million ISK)
Mass Production/ Advanced Mass Production, both increase number of Manufacturing jobs you can run, Advanced at 20M for the book means make sure you need it (ie will have 6+ jobs running at all times to make it worthwhile)
Supply Chain Management (needs Mass Production IV)- you can manage without this skill having it just makes things easier, the more levels you learn the further away from your manufacturing base you can start jobs Level I same system, every level after is +5 Jumps until at V full regional coverage.
As Mang says there are many other skills needed for Manufacturing.
Ships do indeed need the starship engineering skills and encryption skills, those need dedicated Learning plans so only go down that route if a) your doing research as well, b) exploration is your thing (exploration works well as a crossover for research/ manufacturing types) or c) you want to build those nice ships
Rigs need the skills required for using them to build them (doesnt make sense to me but that is what we have to play with) so JUry Rigging III and then the necessary rigging skills.
T2 manufacturing could take a while so ill simplify, lots of Science skills at level III (at 7-10M a book a severe money and time sink (just look at Constantines Wallet to see, and ive not finished yet), good thing is that this also means you can farm those R&D agenst as part of the training plan for datacores, also means you will be a dab hand at invention.