Galaxy clusters provide an avenue to expand our knowledge of cosmology and galaxy evolution. Because it is difficult to accurately measure the total mass of a large number of individual clusters, cluster samples are typically selected using an observable proxy for mass. Selection effects are therefore a key problem in understanding galaxy cluster statistics. We make use of the \((2.8~\rm{Gpc})^3\) FLAMINGO hydrodynamical simulation to investigate how selection based on X-ray luminosity, thermal Sunyaev-Zeldovich effect or galaxy richness influences the halo mass distribution. We define our selection cuts based on the median value of the observable at a fixed mass and compare the resulting samples to a mass-selected sample. We find that all samples are skewed towards lower mass haloes. For X-ray luminosity and richness cuts below a critical value, scatter dominates over the trend with mass and the median mass becomes biased increasingly low with respect to a mass-selected sample. At \(z\leq0.5\), observable cuts corresponding to median halo masses between \(M_\text{500c}=10^{14}\) and \(10^{15}~\rm{M_{\odot}}\) give nearly unbiased median masses for all selection methods, but X-ray selection results in biased medians for higher masses. For cuts corresponding to median masses \(<10^{14}\) at \(z\leq0.5\) and for all masses at \(z\geq1\), only Compton-Y selection yields nearly unbiased median masses. Importantly, even when the median mass is unbiased, the scatter is not because for each selection the sample is skewed towards lower masses than a mass-selected sample. Each selection leads to a different bias in secondary quantities like cool-core fraction, temperature and gas fraction.