How strict are F2P restrictions this time 'round?
Consider it 'free to trial'. You're never gonna make big on an alpha. You're restricted to the lower 3 ship classes, with the 2 biggest locked out, and ALL capitals locked out. You're also locked out of T2 gear, which makes a world of difference. You can fly faction ships, which are better than standard T1 ships, but they're not as good as T2. You've also got 1/2 skill training speed and I'm not sure any useful skills are allowed up to 5. So an omega account that's like 3 weeks old is probably going to out-perform a maxed alpha, just because that omega could be running T2 frigate fits.
The main benefit of the new alpha clones is 1: You can trial forever, instead of the 21 day limit, so you can keep pestering the game. 2: If you lose omega, you can still alpha, and you might have some omega assets you can sell off to get the money to go back to omega.
But really, an alpha isn't going to reasonably get the isk to buy plex. You can probably sub for 2-3 months and be in a position to isk it after that, but not from the start. Incursions are a good choice right now, as The Valkyrie Project (google 'eve tvp') has standard fits and skills for running sites. It's kinda boring, but it's 120m-250m per hour (31.5mil per site). Current plex is sitting a bit above 1bil, so in 4-8 hours of solid running you could flip a plex. But you gotta get there first. They run pirate battleships, which usually run ~800mil with fittings, and take a month of two to get into.
I would suggest learning cloaking first, THEN your incursion ship. While you're waiting on the skill training, you can fly an exploration frigate with cloak and try to make some money in null peeking at data and relic sites. Most of null is just empty, completely lacking people, the populations are centered around gate campers and home bases, and those are easy to locate if you view the map by pilot numbers. So just wander into null sec, either through a non-camped route or through a wormhole, then start scanning things, and if someone shows up in local you can just tap cloak until they leave. Remember - if you're between 2,000 and 5,000 of a hacking site, you can right click your data/relic tool and set 'auto-repeat' to OFF, then when you cloak it won't stop your hacking. BUT if you click any hacking nodes it'll fail. So you can sit halfway hacked and cloaked until you un-cloak, and then you can resume hacking.
By running exploration sites you can make up the isk to fit your first incursion ship, and then the isk flows like water, and you should figure out another isk-making activity, because incursions will wear on you. Or spend 3 days running incursions to pay for your plex and get spare bank, and the other 27 days fitting super cheap frigates and going suicide pvp because you can replace your losses!