The hard truth of this issue is that your stated goals are not achievable solely through skills, and in fact, your skills will most likely have very little influence.
The Skills you want to focus on depend on exactly which part of the Production and Manufacturing chain you want to be engaged in.
Starting from the very beginning of the production chain:
Here, the important skills you’ll need are those to (1) pilot mining ships, and (2) utilize harvesting equipment and upgrades.
Ship skills would include Mining Frigate, Mining Barge, and Exhumers. Equipment skills would include Mining and Mining Upgrades.
If you want to mine more specific Ores, for example, Mercoxit, you’ll also need to train Deep Core Mining.
The second step in the production cycle is to Refine the Ore that you have mined. This is a very important step and is often where most of the margins are produced. Refining is the act of converting raw Ore into Minerals for use in production.
In the Resource Processing skill tree, you’ll notice dozens of “Processing” Skills. These skills will increase the refining Efficiency when your character refines ore of that type. For example, Spodumain Processing gives you +2% bonus in reprocessing yield per level, for a maximum of +10% at Level 5.
It is important to note that at this step, there are several other factors beyond just your character’s skill. The station that you refine at may have its own bonuses (for example, an the Refineries class of Upwell structures can each be fitted with Rigs that increase Reprocessing efficiency) as well as certain Implants.
Keep in mind that oftentimes, you’ll have to pay some amount in fees in order to utilize a Refining service.
For reference, at base refining, you’ll only be able to recover 50% of the Ore’s maximum Mineral output. At (near) perfect, you’ll be able to extract around 84%. That 34% comes from Skills, Implants, and a max refining rigged Refinery, so it’s not something that’s easily accessible, but will net you some nice margins for profitability.
The third step in the chain is production. The skills you need are Mass Production and Advanced Mass Production. These two skills will determine how many Production slots you’ll have access to.
The rest of the skills are nice, but fairly specialized. For example, all of the Advanced Ship Construction skills are specifically for T2 Ship hull production for that ship size (for example, Assault Frigates are considered Small ship, Recon Ships are considered Medium).
Keep in mind that as to your stated goal of “generating an income” this step requires that you do a fair bit of research. Simply producting whatever you feel like will not mean there are people who will be willing to buy.
You’ll have to spend some time researching the local markets, checking their prices and determining whether you can produce ships with enough of a margin to make it profitable for you.
If you already know what you want to build, then that’s good news, because you can proceed to the Blueprints.
You can purchase Blueprint seeded by the NPCs at various Stations around empire space, but they’ll generally be geared towards those of that empire’s many naval faction. For example, if you want to build Gallente ships, you’ll only find Blueprints for Gallente ships seeded in NPC Stations in Gallente space.
These Blueprints are considered “clean” blueprints, as in that they have not been Reseaerched yet. Blueprints have 2 aspects that can be improved by players. These are Material Efficiency (ME), and Time Efficiency (TE). ME reduces the total amount of input materials consumed by that amount, while TE reduces the total duration of the production job by its amount.
For example, if you have a 0 ME and 0 TE Blueprint that consumes 100 Tritanium and takes 60 minutes to complete. A blueprint with 5 ME and 5 TE would consume only 95 Tritanium and take 54 minutes to complete.
In order to research these Blueprints, you’ll need to have trained the Laboratory Operations and Advanced Laboratory Operations skills in the Research skill tree. These will increase the number of Research job slots that you have.
Blueprints can only be researched up to a maximum of ME 10 (for a total of 10% Material efficiency) and TE 20 (for a total of 20% reduction in build time).
Finally, once you have mined your ore, refined it into minerals, and produced your goods. You’ll have to sell them.
Here, the only real skills you need are those that provide for Market Slots, such as Trade, Retail, Wholesale and Tycoon. If you would like to engaged in Contract work, the aptly named skill Contracting is what you want.
The rest of the Marketing skills are nice to have and can be used to help supplement any of the previous steps in the chain. For example, Broker Relations can help reduce the Brokers Fees that you incur when setting up a Buy Order in NPC stations. This can help shave off some margins when you want to purchase some Minerals or Ore that you’ll use to Produce or Refine.
If I can #realtalk for a moment. You will never get a “solid income going” from doing production as a solo pilot. You’ll be competing against hundreds of other players, many who have alts or have social connections that boost their positions.
It’s all too common that some new(er) player joins the game with visions of grandeur, but the thing is, Production and Manufacturing is ultimately a numbers game. Every bit of margin you can save and every slight expense you shave off at each step of the chain adds up to make profits.
As a solo pilot, you’ll spend a couple of hours mining only to find out that you’ve gotten enough ISK to build a destroyer or two. Then when you build 'em, realize that people are already selling them for 8-10% below what you need in order to just break even, let alone profit.
If you really want to get into this kind of gameplay, you’re going to need to join a corporation that specializes in in so that you can take advantage of the numbers and services their offer for you.
Good luck, but I wouldn’t put my eggs into this basket as a solo pilot.