It mostly depends on how fleshed-out the campaign world is. If all I know going in is, "We're gonna play some D&D," then I'm likely to start with a class/race combination and build a concept around it. If I have a clear sense of the world and what the PCs are going to be doing, I'm more likely to start with a concept, list off class/race combinations that fit, and pick one that appeals to me. (Though I do keep the mechanics in the back of my head when picking concept - for instance, I know I'm not likely to have fun playing a straight-up fighter, so I won't pick a concept that locks me into that class.)
The last campaign I played in started off as a one-shot adventure, so I just picked "elf cleric" and made a character. Eventually that character had to leave the party for, um, reasons, by which point the one-shot had evolved into a full-fledged campaign. I made a new character with the concept of "ex-pirate admiral of a besieged port city." I made a list of options for class and race, and settled on half-elf arcane trickster.
The last campaign I played in started off as a one-shot adventure, so I just picked "elf cleric" and made a character. Eventually that character had to leave the party for, um, reasons, by which point the one-shot had evolved into a full-fledged campaign. I made a new character with the concept of "ex-pirate admiral of a besieged port city." I made a list of options for class and race, and settled on half-elf arcane trickster.