I am playing BG1 for the first time, and I got fatigued almost immediately after I set out of candlekeep. What are the effects of it and what causes it?

Also: When I start up BG2 (I have BGT) and it gives me the selection between BG and the BG2 DLC, does it matter which I choose?

You get fatigued if you are awake for longer than 24 hours.
This includes travel time.

Your characters will obtain penalties, but I don't know which ones, on top of my head. Probably they're penalties to AC, Thac0, saves, and such. The longer you stay awake, the greater the pen aslties become. I don't know if you can actually pass out or something.

Fatigue is caused by not resting. The in-game counter is incremented every 4 game hours, and is adjusted to account for Constitution: characters with high CON get fatigued less quickly. The actual calculation is thus:

nFatigueLevel = nGameTime - nTicksLastRested / 4 hours
nFatigueBonus = GetFatigueBonus(constitution)
nFatigueLevel = nFatigueLevel - nFatigueBonus >= 0 ? nFatigueLevel - nFatigueBonus : 0

What it actually does after all the math is to change the Luck modifier, with a consequence to everything that Luck affects, such as saving throws, morale etc.

When you start BGT, if you want to play BG1 you must choose Baldur's Gate. If you want to play BG2, skipping BG1, you must choose 'Start a new BG2 game'.