Each skill has five levels, and that's it. Each level of skill gives the same amount of benefit (well, except module unlocking), but each level costs more and more. This generally favors getting a skill to 1-3, maybe 4, but leaving 5 for later.
Here are the individual base SP costs to unlock each level.
Level 1 6,220 SP
Level 2 18,650 SP
Level 3 43,530 SP
Level 4 87,060 SP
Level 5 155,460 SP
(or a total of 310,920 SP to max out a skill)
However, each skill also has a multiplier value. This can be from 1x to 12x, and you... multiply the base cost to find the actual SP needed to raise a skill. Key skills are 1x, most infantry and turret skills are 2x to 5x (though there are four 6x and 8x, heavy weapon enhancements and suit unlocks, respectively). Vehicle skills are the expensive ones. If you want to be a tank driver or dropship pilot, you really should consider paying for SP boosters if you want to get them up in a reasonable timeframe. Also, vehicles are EXPENSIVE in ISK, and except for a single LAV (jeep), none of them have BPOs.
Most skills cascade from others, you'll need a minimum level in a previous skill to start leveling the next. (The skill to boost your shield HP is kind of deep, whereas the skill to boost your armor HP is a key skill.)
The current skills come in nine major categories. In addition to unlocking modules, most include a small effect bonus.
Dropsuit skills, which unlock advanced suits and stamina boosting modules.
Circuitry skills, which involves CPU, sensor, and hacking modules, and most equipment.
Combat Engineering skills, which involves PG, and shield modules.
Field Mechanics skills, which involves Armor modules, and repair tools.
Two large groups of Weaponry skills, one which unlocks and enhances specific weapons, and another that enhances categories of weapons (heavy/light/sidearm).
Vehicle Skills, which unlock advanced vehicles
Turret skills, which unlock advanced turrets.
Corporation skills, which lets you act as CEO, and increase the maximum membership size of your corp.
For now, your skilling choices revolve primarily around increasing your weapon performance, or your defense. You can also skill into stronger equipment, improved running, hacking speed, and sensor strength. Also, at the same time you're going to have to spend a bit on skils that improve your ability to fit things.
Which you go for is largely up to how you play. Damage is always a good choice, especially if you never get hit. If you're dying all the time, more HP might be for you. If you happen to find you have a talent for staying out of combat and sneaking around capturing stuff, stamina and sensors will just make you better.
For now, I would suggest using an alt if you want to start a corp. That 300k SP, combined with a day (or twos) worth of active SP is enough to get the number of people you can have in the corp up to the 50-150 range, should be enough for anything short notice.