Low level missions are pretty easy. You should be able to just about walk through them as you learn the game.
Train your Learning skills
as soon as you can make that NOW! Take them to 3 or 4. Then you can rest them for a bit as you get your pilot skills up. Some say to take all the basic Learning immediatly to 5, but that takes for-ev-er.
Mining in secure space is nice at low levels as well. You won't get rich, but you'll be able to steadily upgrade you ships.
Do NOT try to PvP untill you can afford to lose everything on your ship. EVE isn't a normal MMO. Your ship gets blowed up, it's gone. along with your weapons, ammo, everything. On that note: INSURE your ships! For as much as you can. Then you don't end up with a complete loss.
Ummm... Oh, careful when buying things on the market. sometimes folk will sell things for ridiculous cheap prices in 0.0 space. That can be a bad place alone.
Edit: Two more things. Keep your clone as up-to-date as you can afford. You die with more skill points than your clone is rated for, you LOSE them. That sucks.
and find a way to maximize your training time. You accumulate points in real-time. Even while logged out. So, train your short 30-60 minute skills while playing and set long trainers when you leave for school/work/whatever. I actually used an electronic kitchen timer to keep track. Even woke up in the middle of the night if I had to so I could set a new skill. There is a program...
EVEMon. Use it. it is an out-of-game monitor. You can check your skill training without actually logging in. Excellent tool.