Training a second character is inherently easier than what you went through training the first. For one, you know what the hell you're doing from the beginning and have a plan from the get-go.
You're also likely to be able to support the new guy with the resources needed. A skill costs a few million? No problem... cash transfer, and a few clicks later you're training Exhumers. Implants? Sure, full set of +3's from day one. Your second account tends to train much faster than your first.
A few months ago I started along this road as well, started anew with a Caldari Civire guy on a second account. I didn't start with a Military profession, as this is something I could mold him into on my own. Mostly I picked a Civire based on the fact that I didn't like the other races' mugs any more - atleast Civire look remotely human, hehe.
So I started with the Prospector profession, as I wanted to train a hulk pilot and not waste time for this on the other account. So for 2 months and change he simply sat berthed in a University station in The Forge, churning away at getting the skills needed to fly a decent rock buster. Interestingly enough, the starting skills included everything needed to use T2 Modulated Strip Miners (with T2 Veldspar crystals), all that was needed were the skills to fly the ship and various odds and ends to make it all fit, like mining upgrades, Mechanic etc.
I also trained a couple of levels in Corporation Management so I could start a one-man corp in order not to have to listen to all the newbie chatter in the Deep Core Mining channel every time I logged in.
After 2 months I was looking at a character sporting 3.6 million SP (If I recall correctly, Brutus only hit 4 mil SP four and a half months after creation). A quick 100 mil transfer from Brutus' wallet later, he had a fitted hulk (minus the rigs, for now - forgot about them when I bought it). He's far from a perfect miner, actually he's quite bog-standard, I trained for this just to prove to myself I could, but anything else, like additional t2 crystals can be trained on-the-fly. Now comes the real skill plan, focused on ship and weapon skills.
Even though he's Caldari, I do not plan training this race further than frigates. Instead, he'll focus on becoming an Amarr ship pilot. Not to disrespect Caldari pilots, but I tend to believe the best defence against incoming rounds of ordinance are heavy plates of hard alloy, not shields, and the best weapons are those that cause pain when you press the trigger as opposed to half a minute later - but that's just me, don't pay too much attention to it.
As opposed to my first character, I'm in no hurry to step into a bigger ship. I know how a battleship blows up, just as well as I know how a frigate blows up. So first - support skills, and lots of them. To level IV at least, preferably maxed out in the long run.
