loss of power, rough idle, cutsoff when idling

I i recently purchased a 87 535is from s friend that has kept up with fantastic maintance, i had to drive the car almost 3 hours from Richmond VA it did phenomenal the whole drive, but now that i get it home it sits for most of the day but recently actually yesterday i was cruising around 40 then i went to accelerate and it wouldnt accelerate so i gave it more gas and it still wouldnt until i floored it it jumped and knocked into speed. i came up on a red light & at the red light the idle has never been rough at all but at the red light it started shaking so bad it cut off on me so i quickly started it back up and it took forever to get over 25 mph idk what it could be i just want someone to tell me a list of possible problems

Fuel filter, fuel pump, fuel pressure. But there are may more.......................... Start with the easy stuff.

Also check the plug wires never know. mine did the same thing and it turned out my number 6 plug wire was crap

Remove injectors for ultrasonic clean and flow check.