Erm, phew. Where to start...
First off, do not mine. It's easy money to begin with but if you head down that route one day you'll realise you watched a mining laser zap a rock for 3 hours straight and it'll make you cry.
You want to get a source of ISK sorted as first priority, which is probably going to mean mission running, at least to begin with. Try to keep your initial training focused, as there are a lot of skills and being terrible at many things doesn't really help. There are a few you should invest some points into like the social ones (they make agents like you more) but really, pick a race whose ships you like and focus on skills that make the smaller of that races ships better. There are a lot of support skills that are ideal to train once you've picked a race - they all look a bit uninteresting on the surface but all those +2% here and theres add up quickly and so they're actually key and they're also essentially ship upgrades you carry in your head.
Caldari tend to be the most
common mission running ships, partly because Caldari are the most common race but also because most of them use missiles and missiles are the better weapon for pve. (Because they don't use tracking.) They're not too common in pvp though other than for ECM use because missiles aren't too hot for pvp because of the way they work though they're not terrible. They also almost always shield tank, which is great for pve but for various reasons isn't necessarily great for pvp - although drakes (one of the caldari battlecruisers) are solid pvp ships in gangs as well as pve.
Gallente ships are (in theory) mostly short range brawlers, there are exceptions but thats pretty much what blasters aim to do. The jury is out on whether they actually achieve that though, as they're up for a good tweaking in the winter expansion. Gallente ships also tend to use a lot of drones and mostly armour tank, and many of the ships have bonuses to armour repair or drone health/damage. Gallente ships also commonly look like
potatos.
Minmatar ships are a bit of an odd mix especially as they've got both missile and projectile weapons (often on the same ship) and some of their ships shield tank whilst others armour tank. This makes them very flexible but also potentially a real pain in the arse to train as other than the ship specific skills you'll need to train *everything* in order to use the full matari ship line up. Of course you don't have to be able to use every ship and theres no reason you can't mix and match between the races. Matari ships tend to look like
rusting heaps of scrap although they also have a
star destroyer.
Amarr are
clearly superior, what with being
golden plated laser toting ships, but they're also not generally as flexible as the races - which is one reason they make
good fleet ships. As with all the races there are some exceptions of course.
Frigate wise, the best ones for general pvp are either the matari rifter or the amarr punisher. Both lines expand nicely for opposed pvp as well, with matari probably having the edge for random solo stuff just because they've usually got more mid slots - which is what you use for EWAR. Amarr ships tend to have less mid slots and more low slots (which are usually the tank/damage mods), so are usually the heavier brawlers with the matari being the nippier fighters. honestly there isn't much difference in effectiveness between them though, they just do the job in different ways.
Later on there are lots of alternatives to missioning to make your money but they all need some form of investment in either ISK or skills, usually both.
Short version would be to avoid mining, do some missions to get an income going and then start training for something small that you can muck about with in pvp (either in lowsec or join a militia) cheaply without worrying about exploding - because you will explode a lot.
If you tell me who you are, I can give you some ISK to get started with - even if you're not amarrian!