Specialization

You probably want to do this, ideally with other players, but this can also be done with multiple accounts. The problem here is there is too much for any one player to do (unless they are a very old account or otherwise have a lot of skill points) so splitting various roles out across multiple accounts makes sense. A single account can handle some of these roles, e.g. someone who does mining will also have Industry skillpoints suitable for manufacturing. Possible roles include:

General Roles

• DPS - someone in PvP needs to apply damage to make ships go boom. Overlaps with Tackle roles, maybe PvE missions, and over combat roles, though specific fits will vary depending on the type of combat—solo PvP? gang or fleet with a doctrine? suicide ganking? other?
• EWAR - specialized combat role similar to logistics but with different skills. What works here may depend on what works for you or fleet doctrine, and may require a larger gang, as a gang invariably also needs tackle and DPS to come from somewhere, which electronic warfare or logistics ships probably do not supply.
• Exploration - scanning and hacking skills. Probably wants cloaking and especially navigation skills. Explorers can also work as "eyes" for a fleet or gate camp, or they might light up cynos for other things to jump to.
• Fleet Command - specialized PvP (or even complicated PvE mission) support, probably best grows out of various combat roles or possibly exploration. It looks like they've added a bunch of fleet skills and ships since I last played in 2014.
• Hauling - Space trucking. Handy if you end up with lots of loot that needs moving hither and yon. Or corporations may pay you to do this in their nullsec holdings? The scale here can vary between low-level Distribution missions to cyno jumping some huge ship somewhere.
• Industry - overlaps with Mining and Resource Processing. I haven't gotten into the T2 manufacturing thing which probably requires all sorts of skills and stuff to be good at.
• Logistics - overlaps with various combat roles for the frigate and cruiser skills.
• Mining - overlaps with Industry and Resource Processing. One may also want cloaking and navigation skills if mining in a Prospect is done in lower security systems, and you may need someone to scan down those nullsec gas sites for you.
• Missions - train up for suitable PvE skills. Depends on the missions flown, overlaps with DPS, and logistics or EWAR roles to a lesser extent, as you can't really neutralize capacitor on rats who have infinite capacitor, and shooting them is better than jamming them, usually.
• Resource Processing - there's a lot of skills here, and loss can be minimized by maxing out these skills. Overlaps with Industry and Mining.
• Salvage - loot those wrecks for profit! Salvaging V, a suitable destroyer with expanded cargoholds, and a mobile depot. Best done in parallel with mission running. May pair well with hauling, so you don't have to juggle loot to different accounts, and possibly also Trade (so you can sell the loot) or Resource Processing and Industry (so you can turn the bad loot into minerals and then craft things).
• Tackle - Interceptors and whatnot. Navigation skills overlap with the Exploration role, or can develop heavier tackle (Interdictor, Heavy Interdictor) or other combat roles, PvE mission running, etc.
• Trade - may need Hauling to get corporation and faction standing high enough to minimize fees on transactions. Distribution missions could be done by flying alongside a Hauler alt, but that's more work.

Most characters will need at least a little of PvE combat skills, as that can take you though various missions for faction standing gain. Or you can sit in a station all day and trade, you do you. Alas, most of my characters started out before I learned all the above and the benefits of specialization, so they tend to be somewhat cross-trained and have skills a bit all over the place. Currently there's the exploration account (really good scanning skills, covert ops, Sisters of EVE ships) which being the oldest account also has skills all over the place; the combat account who flies a Sabre real good and battlecruisers too for PvP or PvE but also has some industry, trade, and resource processing skills; and a third account that is newer and mainly does mining and hauling and salvaging. Industry and trade and resource processing might ideally be done by a fourth account, or maybe you can find someone with perfect refining skills and get the goods to them.

Speaking of space trucking, there's a song for that (and a Cowboy Bebob episode).

Yoko Kano. "Live in Baghdad".

Specific Fits

Another method, used in addition to core ship fitting skills, is to train into a specific ship to be really good if not perfect at that ship. Usually this will be to fill some doctrine fit, e.g. to be really good at flying a Sabre, which will require good navigation skills, Interdictors V, excellent gunnery skills, and so forth. Once perfected (or "good enough") another ship fit would be targeted, possibly alternating with core skills, as more advanced ships like a Vagabond require higher levels in core skills. Ideally the ship types should have some overlap, though you may end up with PvP and PvE ships that do not share weapon systems. Such is life. A downside here is knowing what you want to fly and going for that, which may not be possible until you try out a ship or a role to see if it works for you. Maybe focus on core skills early and use the skill assistants to try out various ship types and roles so see what works for you?

Another option is to train "good enough" and fly in a gang, where numbers will help make up for any lack or perfection of various skills. This is less of an option for someone who flies solo, as in a one-on-one fight skills may be the deciding factor, though of course better manual piloting (distance of engagement, speed, etc) can also make a difference. "Good enough" skills will let you try out a variety of ships, or fly for variety if what you fly depends on what mood you are in. This may not be the most ideal for ISK maximization or skill perfection, but could be more fun.