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I played Eve back at release, almost 5 years ago. I left and came back several times with the trial, I only had a subscription added to two of the many accounts I used but I learned alot about starting the game.
1. Research is key.
Know what you intend to do and how to play. Find out what type of work you will be doing and how you would like to do that work. IF you can answer those questions you can probably choose a race and starting skills that puts you well on your way to doing that.
2. A man's reach should always extend his grasp.
Pilot what you can afford to replace, don't invest heavily in something your unsure of. This may seem like common sense but how many people plan to say, mine until they can afford a bigger ship then jump headfirst into missions. Or the opposite, run missions until they can afford an industrial and begin jetcan mining.
I'm not saying you can't switch up what your doing, I'm warning you that throwing money into the unknown can hurt. Also someone who has been running missions and has a nice frigate for quality level 1 missions probably doesn't have mining skills and if they forgot rule number 1 they probably don't know how to outfit a ship to do so.
Someone who has mined up to a cruiser may have trouble with level 1 missions when their tracking speed doesn't quite shoot at frigates and they probably won't be able to do level 2 missions where their cruiser probably belongs for a while.
Make minor investments to test waters, there are very few areas of eve available to a beginner where you aren't paid proportionately to how long you've been training for something or how well you do it. If you take a smaller ship with a minor investment that you can throw away or lose in combat you can get a feel for weather or not you can suceed at the new line of work.
3. Friends pull you through hard times and give you new opportunties to learn and profit.
If your ship gets blown up, if your ores gets stolen, whatever, your friends will be there to help you pick up the pieces, or atleast make light of it and give you sugestions so it doesn't happend again.
As for the new experiences- How better to learn how missles work than having a buddy who spams missles as his main weapon? What does he have difficulty with and what does he do well against? How better to learn how to get the best prices for your ore than know a manufacturer?
4. Learn from others, Conform to sucess and take everything with a grain of salt.
There are somethings that general wisdom hold to be true. Not all ships are created equal, some items are worth more than others. Learn from the academy corp that you start off in. If everyone is running missions in a rifter maybe you should too. Conforming helps get you by when you don't really know enough yet, but when the time comes there are different schools of thought. Some people think the way they do because of what they do and you should notice this. Someone who has spent a year in the academy probably has different views on low sec and making money there than someone in an alliance. Like wise someone may believe something false like their ship being underpowered or you "need" a cruiser for level 2 missions because it takes the blame away from them.
With that out of the way I can give specific advice on what you should do.
Here are the necessities:
Complete the tutorial atleast once
Complete the missions given to you by the agents you are refered too. You will get your first two ships, some equipment and a grasp of the different mission types from these.
Read the official website's playerguide, it will explain alot.
Here are things that will help greatly:
^^ a guide to attributes, read these BEFORE creating your character and you should have an idea of what to do. The second link is basic builds with an explanation. Keep in mind your character will change greatly from this as you learn skills.
A couple guides on things every player should know and a list of npc resistances/damages and mission type % per field of agent.