The performance of a multimode fiber optic surface plasmon resonance (FO-SPR) sensor has been studied, both theoretically and experimentally, as a function of three crucial parameters - metal layer thickness, tapering ratio (TR) and fiber surface roughness. A combined approach is adopted to investigate the effect of these three parameters on FO-SPR sensor performance instead of considering them individually. Intriguingly, the three parameters are found to be highly correlated and their combined effect significantly influences the FO-SPR sensitivity. It is observed that optimum gold thickness to attain maximal sensitivity varies for different tapering ratios. Moreover, increasing the tapering ratio does not always increase the sensitivity as claimed in previous studies, but instead depends on the fiber surface roughness generated during chemical etching. The optimized FO-SPR sensor exhibits a high sensitivity of 4714 nm RIU <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> with standard glycerol solution in the refractive index (RI) range of 1.372-1.388. Furthermore, the optimized FO-SPR sensor has been employed for label-free detection of bovine serum albumin (BSA) and parathion pesticide. The system is able to detect BSA concentration as low as 1.5 pM and the parathion pesticide is detected at 0.1 ppb levels.