Just a quick question. When you finish a shift on LCPDFR, do you go back to your safehouse and save your game or just quit? I always just quit the game but should I save it?

I just exit the game. If you arrested anyone or anything like that it should automatically update your stats like you have in your signature. Other than that I don't really think it matters unless you want to save any progress that you made in the game. 

Yeah, I know it saves all your stats. I was just wondering as people seem to save their money looking at videos and pictures they upload. Was also thinking if I save game with weapons and in police uniform, would I start the game with weapons and in police uniform?

I had tried that and It never seemed to work for me. Whenever I would load back in I would just be regular old Niko Bellic. It doesn't save your uniform or weapons that I know of. 

If you save the game in police skin, it corrupts the save, and you can't recover it (need to delete and start over).

Never save games after playing LCPDFR. It will corrupt your save file and make it unusable, you will have to start a new save file which means that you'll lose any progress in the storyline.