Agreed, start with the fuel question. Start forward, and cheapest and work back.
Primary fuel filter.......is it clear with no debris?
Secondary fuel filter.....when was it changed last?
Priming pump....is it the old style (white top) and does it leak at all?
Fuel tank screen.....connect a portable tank and see if the problem goes away. If so, you may need to drain the tank and clear the fuel screen.
Most of these are fairly easy repairs (the tank screen takes a bit more but it isn't difficult). If the car sat for quite awhile before you purchased it, the fuel system may need to be gone through. Any debris found will certainly be a red flag.

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Sam

84 300SD 350K+ miles ( Blue Belle )