Another question: What are the main differences between BFRPG, OSRIC and Labyrinth Lord? Which of the three would best fit my playing style?
OSRIC is a clone of AD&D 1E. It fits some points (low prep time, plays fast) on your playing style, but is the most "rulesy" of the Old School games (might have to refer to the manual a fair amount).
BFRPG I'm not too familiar with. I think it's D20-related?
Labyrinth Lord is a clone of Classic D&D, which means of the Moldvay/Cook or Mentzer versions of "Basic & Expert" D&D... in this case I believe the game sticks closer to the Moldvay version. It fits your play style to a tee except for allowing strange race/class mixtures (though that's not hard to add, but it would require say an hour or so of writing up rules for it).
My own suggestion would either be Labyrinth Lord or Swords & Wizardry (Classic D&D or OD&D, essentially). They both play very fast, the rules fade almost entirely into the background and prep time is at the absolute minimum. With both the one bit of work you'd have to do for your play style is to allow Demihumans to take a variety of classes... perhaps.
What I'd suggest even more than those would be to go to RPGNow and buy the $6 PDF of the OD&D core books. The rules are fast and loose and open to your interpretation. There is no Thief class... and there doesn't need to be! You find things by looking in the right place. Do you see the button in the sarcophagus? Yes, if you climb into it and search it carefully... otherwise no. Can you disarm the trap? Well, I'll tell you how it appears to function and you tell me what you're doing. "Class" doesn't need to define everything about a character.
What I like about OD&D is the simplicity of the stat block:
Pyro-Rodent: AC 7, HD 1, Move 8", spit fire for 1d3 in 10' cone
Or for a more basic monster:
Dire Stoat: AC 6, HD 2, Move 15"
Simple, eh? You've got a few basic mechanics, and the freedom to build your game around that in whatever way you choose. Your Kung Fu will be strong!