Scintillations are found for incoherent general type beams in weakly turbulent horizontal atmospheric links. Incoherent cosh-Gaussian (IChG) and incoherent cos-Gaussian (ICG) beams exhibit lower scintillations for larger absolute displacement parameters. IChG beam yields lower fluctuations than the ICG beam for the same absolute displacement parameter. Narrower ring incoherent annular (IA) beam scintillates less than the wider ring IA. Increase in the source size lowers the scintillations for all types of the incoherent beams. As the wavelength increases, the scintillations of IChG, ICG and IA beams first increase, then start to decrease and eventually the scintillation indices merge towards a certain value. Raising the structure constant first increases the intensity fluctuations for all the mentioned beams where further rises in the structure constant result in the same level of scintillation index.