I'll start you off with the Manufacturing Side.
'Industry' - 4% reduction in Manufacturing Time.
This isn't needed that much if you only want to build 1 thing at a time, as everyone can build 1 thing at a time. But it is needed at level 3 for Mass Production and Production Efficiency skills.
'Mass Production' - Lets you build more than 1 thing at a time, Mass Production 5 will let you build 6 jobs at the same time (the char's basic 1 plus the 5 you get from the Mass Production skill to level 5)
'Advanced Mass Production' - this is just an extension of the Mass Production skill, it doesn't do anything apart from give you extra build slots to use (although strangely it's needed to compress ore/ice in a rorqual too!)
'Production Efficiency' - THE MOST IMPORTANT skill if you want to build things, if you look at a blueprint and see the mineral requirements, you will see You and Perfect columns, the Perfect column is what you need if you've got Production Efficiency 5, it's takes about 2 weeks to get from 4 to 5 depending on your attributes, but if you want to build things on a regular basis then it's essential, it cuts down on waste and therefore saves you money.
Personally I think to start manufacturing you want to be looking at:
Industry
5 (I know I said it wasn't that important, but it's only a level 1 skill, and it will save you isk, if you're building in a station then you pay for the time it takes to build)
Production Efficiency
5Mass Production
4At that point you will be building up to 5 jobs at a time, building them as fast as possible (without plugging in implants and using a pos) with no extra waste (blueprints have got waste which is reduced or eliminated by researching them for Material Research but that's a whole other subject)
You can take it further by adding Advanced Mass Production, in theory you can build 11 things at a time by having Advanced Mass Production 5 (it needs Mass Production 5) so you get your char's basic 1, plus 5 for Mass Production, and another 5 for Advanced Mass Production, but most people stick at Advanced Mass Production 4 since it takes a long time to get it to 5, and it's often quicker to train up another char if you need extra building slots.
As for the mining, I'll let someone else answer that, you might even find that it's not worth the hassle of mining if you can run level 4 missions, but the mineral market is all screwed up at the moment.
Hope this helps
