This game is designed for people to use one character for everything. You can have multiple characters if you want to, but you don't need more than one.
There is an item you can buy from your Grand Company (after you choose a company, around lv20) that will let you reset your attribute points.
Each class has its own attributes, independent of any other. You can freely switch back and forth between physical and magic jobs without either affecting the other.
To be effective in endgame, you will actually need to level multiple classes. Each job has two secondary classes associated with it from which you can use cross-class abilities. It's not a major concern for leveling up, but for endgame, you will need to have certain of those cross-class skills.
The stat differences between races are minuscule. Choose your race based on the appearance you like.