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The most important skills for a fighter are Gunnery,  Missiles, Spaceship Command and, to some extent,  Navigation, Drones and Learning (actually Learning is important for type of characters and it is reasonable to start learning this class of skills first).
The attributes Perception and Willpower are necessary for any of the above-mentioned groups of skills. In most cases these 2 attributes are the most important ones for a fighter.
Respectively for a fighter it is better to choose a race and bloodline which have advanced Perception and Willpower by default.
Taking a look at the table of races and bloodlines, we will observe the following: The Amarrs have serveral bloodlines with advanced Willpower and weak Perception on the other hand. The best Amarr combat bloodlines are Khanid Cyber Knights (PER11/WIL8), Khanid Zealots (PER8/WIL10). But generally they have fairly weak memory, which also an important attribute.
The Caldari have fairly strong Civire Mercs (PER9/WIL10) and Civire Dissenters (PER9/WIL8), but they also have the same problem with Memory, thus the best Caldari fighters are Achura Monks (PER9/WIL8), only having weak Charisma which is not a very important attribute.
The Gallente nearly do not have a bloodline with balanced Perception and Willpower except for  Jin-Mei Jing Ko Caste (PER10/WIL7) which also have strong Charisma.
And finally the Minmatars have Brutor Tribal Traditionalists (PER9/WIL10) and Brutor Slave Child (PER11/WIL9), which are a very good choice for a fighter. The whole race has also fairly strong Charisma (allthough not so strong as at the Caldari).
Besides default characteristics there are also 5 attributes point, which can also ba used for Perception and Willpower, thus you will have fairly good potential fighter from the start of the game.