1999 bmw m3 coupe help having a problem

I just baught this 2 door fantastic m3 and i love it. It rides amazing handles even better power is all there no loss at all every single thing on the car works i mean i have had it for 1 month and no problems at all its flawles. BUt one thing i cant figure out and i need your help. On some days the car takes 2-3 tries to statrt up and some days it starts up right away. On cold days it seems to start up right away sometimes strong and sometimes weak but when it starts as soon as it catches even on a weak start up when its on its amazing. As soon as it starts its perfect. No check engine no codes nothing at all .MOstly on hot days i have to try a couple of times for it to start but as soon as it starts its PERFECT the only problem is the starting part. Where should i start the oil is good i just changed fuel filter it didnt help, the coolant is on point i always put 93 gas in my car. what do i do now, im sick of having to try2-3 times to start the car and than when it starts its like a brand new car. please give me any help any feed back. I was thinking fuel pump or fuel pressure regulator. If i can solve this my car will need nothing it rides like a new car as soon as it starts no problems at all. Only thing i can think of is i get the low coolant error a day or two out the week sometimes more once i shut off the car even though my coolant is topped off and is perfect, i know ill probably need a coolant level sensor but i dont see how that can give me starting problems