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I'm currently in my third experience with starting EVE. I tried it when it was young and quickly gave it up. It seemed too slow. Combat was tedious and travel seemed to take forever. I think I quit within a week of starting.
I tried it again about two years ago. This time, I tried to get in to mission running. The missions I could get were too easy and rewards were tiny. Hunting pirates in asteroid belts was boring. I tried to make my way to more challenging pirates in low sec space. I was set on repeatedly and reduced to bankruptcy replacing ships lost to players. I quit in frustration in the first month.
I decided to give it a look once more in late October. My intention was to just waste some time till POTBS came out. Now, POTBS remains unordered and I'm looking forward to playing EVE for years to come.
Here's what has made the difference for me and will hopefully make a difference for other new or returning players:
1. Making ISK: I found a way to make enough ISK to keep me in the best ships my skills can buy. I set my sites early on hauling trade goods in high sec space. I trained for industrial and had it about one week after starting the trial. It took subscribing to train it, but I had already planned on subbing to give the game a decent look. When I got my Bestower (yeah, I'm Amarr), I had 300k in my wallet. After one day, I was at 12 million. I had mastered the safe routes in my region and kept my eyes on the market for the goods I know would profit me the most per jump. It was interesting and seemed much deeper than past MMO experiences I've had.
2. Mission running: Next, I wanted to always be able to get a challenging kill mission to break up the routine when playing the market and trade route running. To do this, I built my character around social skills. This gave me a huge leg up in agent level and quality. I could instantly get level 2 missions when my newb destroyer or cruiser needed a challenge. Finding a good system for running missions helps. I'm at Stirht. Once station in this system has eight agents from the same corp, so building up standing and loyalty is quick.
3. Player corp: I joined an empire player corp early. Noob chat was a horrible intro to the game. 2000+ people trying to ask questions, answer questions, or spam sell ISK was pointless. I got in a friendly corp that didn't mind pointing me in the right direction for answers. I've got people that don't mind sheltering me on a higher mission or teaching me how to partake in a mining op. I'm developing relationships that enrich the game.
4. Dual acounts: Having a second account has made it more fun also. I picked one up in early Nov. when they had the special going - $40 or so for 6 months. I made my second character combat oriented. Now, I have my first as a mission getter, trade maker, social guru and my second as the meat behind the brains. Working in tandem, I've ran my standings with a big corp up to 6.58. Now, I have mission options coming out my ears.
5. Anticipation: Now that I've taken the time to read up on the game and see some success in the early game, I'm planning the future of my characters and eagerly anticipate milestones they'll soon reach. My trader / social guy will be flying a covert ops contract runner in 23 days. He'll double as a scout the next time my Corp gets wardec'd. My combat spec "alt" will be in his own battleship complete with a T2 drone fleet in about two weeks.
Summary: Starting in EVE is ruthless. Having a character plan to work towards is essential. Do some research of the possibilities before getting frustrated with the early game. Get in a helpful corp early and turn off the newb chat. Understand it's a long haul game. If you find yourself getting bored or frustrated, put on a multi-day skill to train and take a break.