Fuel Pump

So last week the car broke down and would not start. The tow truck driver said it sounded like a fuel pump to him. The next day a mechanic came over to check it out and the car started, he test drove it and it was fine did not break down at all, he said all it needed was some front breaks, tune up, a hose (one had a hole in it and he said it could leak antifreeze), and a catalytic converter. The following day we drove the car, it was fine for about 10 minutes then at the first red light the car cut off. We let the car sit and then it started again. Then at the next red light the car cut off again. It did that all the way back home and when we finally got it home it was smoking under the hood on the left side but the car was not hot. I want to be sure of what it is before I buy a fuel pump and pay to have it put on and it is not the fuel pump. The mechanic said to have the brakes and tune up done first to see if that is causing the car to stall and go from there. If it is the fuel pump, what type of fuel pump does this particular car take I noticed it is two different ones electric in tank and in line?