No, Yes, Sort Of and It depends on what you want.
Which is a very Eve answer.
The bit you now don’t need to read:
A lot of good answers here - basically, if you view this as a game of internet spaceships then your initial character selection has almost no impact - and definitely no long term impact.
There are initial slight tweaks, a Caldari character will have level II in shields and armour, the others have Level III armour and Level I shields, but that is only a difference of a few hours to level out either way - the start just reflects the preference of the Caldari for shield fitted ships.
(in which case why don’t the Minmatar get “sticky tape III” as an initial skill??)
You get basic skills in the faction specific ships, Amarr Frigate I for Amarrian characters and Small Energy Turrets I - the Amarr weapon of choice. But you can buy the other racial weapon and gunnery skills cheaply enough. And you get the skill for the relevant racial hauler so you can lump stuff around if you have the urge.
An Amarrian character starts in Amarr space, Caldari in Caldari space, the Gallente in a brothel somewhere and the Minmatar in a state of general victim-hood. But you can always better yourself - unless you are Amarrian where you’ve started as god’s chosen already (it’s a high perch, try not to fall off it).
There is no limit to who you can attack or defend or your objectives except those you place upon yourself. You drive all of what you do and what you want out of Eve - it never holds your hand and says “your next objective on the step to Hero status is to get the Golden Sword of McGuffinism to enable you to defeat Ming the Not Happy without killing any of the villagers”. Real life doesn’t do that. Why should Eve?
The name you choose when you create the character is the name you will keep for that character for your entire life in New Eden. You may have thought of something humorous, but it’s like naming your son: “Sunshine Moonflower” may have sounded really sweet - but imagine when he becomes Head of Engineering at a respected Technology Company: “Mr Moonflower” signing his name “Yours, Sunshine” isn’t possibly the image he would hope for. particularly if he turns out six-foot five and built like a brick outhouse. OK Sunshine?
You can not change your name, gender or racial characteristics. You can resculpt your body at a price.
The decisions you make in Eve are permanent; there’s no ability to undo or roll-back to a “game save”. It is this that makes Eve a rare game - more like life - and that’s why it appeals to many players.
The first of these decisions is “Who are you?”
There is one important aspect: Eve has a deep lore and history. It is a place where people can take up the role of their character and play it as a role playing game, mentally or openly writing in back stories for their characters. This is Role Play in the more free flowing D&D nature than in the Skyrim pre-programmed paths and options nature. Players engaging freely with a wider narrative. A fair few players do this to a greater or lesser extent with greater or lesser levels of seriousness. The game mechanics of standing with the different factions supports this - work steadily for Amarr and eventually you’ll be PNG’d in Minmatar and Gallente space (stroppy buggers).
There are corporations and alliances that operate on an “in character” basis, engaging with the story-lines reacting and participating in events. Amarrian is probably the most active, but there are groupings within the other races - some of the largest battles in High Security space have been RP driven (and don’t suffer from the “and then someone dropped Capitals on us” problems). Many of these RP player entities will have additional rules that restrict what you may or may not do and are among the oldest player organisations in New Eden - CVA - Curatores Veritatis Alliance - down in Providence are a good example of that: attempting to bring the Amarrian Reclamation to areas of Null Sec. space, but RP groups operate across all securities, hi, low and null, and regions of space.
Well, that became a long introduction and rather more “what is Eve?” than the original question asked.
However if you want to live here, the most important thing I can say is “Welcome to New Eden”.
By His Light and His Will,