Monolayer kagome metals \(A\mathrm{V}_{3}\mathrm{Sb}_{5}\) (\(A=\mathrm{K},\mathrm{Rb},\mathrm{Cs}\)) form a problem of materials design under reduced symmetry, with van Hove singularities nearby, charge order, competing superconducting phases, and Hall-sensitivity within a limited energy interval accessible to strain, gate, and stoichiometric tuning. The question raised in the present paper concerns not whether correlated phases arise in monolayer \(A\mathrm{V}_{3}\mathrm{Sb}_{5}\) but which one should be investigated in the first place, given a particular Fermi level and tuning strategy. For answering that, we develop a symmetry-based order graph whose nodes comprise a type-II filling regime around \(-6~\mathrm{meV}\), a type-I filling regime centered on \(9~\mathrm{meV}\), a positive-filling region near \(35~\mathrm{meV}\), six charge-order channels, two main superconducting channels with even parity, and experimental tools. The edge weights incorporate proximity to van Hoves, \(M\)-point commensurability, local/nearest-neighbor interaction preference, time-reversal symmetry consideration, and monolayer access. A different hierarchy emerges for each channel. The type-II quartet channel favors rectangular inverse star of David and star of David doublet ordering, while maintaining \(A_g\) superconducting order as the strongest competitor. The type-I channel accommodates a more symmetric, commensurate charge order through a wide susceptibility peak contribution. A separation of the Hall-active \(\mathrm{TRSB}\)-2 phase from \(B_{1g}\) superconducting order by the positive-filling channel makes anomalous Hall measurements and pairing-symmetry checks a crucial experimental task. Stability normalization in terms of cohesive energy, the \(4~\mathrm{meV}\) per atom distortion limit, and the exfoliation energy of \(42\), \(45\), and \(45~\mathrm{meV}/\text{\AA}^{2}\) for \(A=\mathrm{K}\), Rb, and Cs leads to \(\mathrm{KV}_{3}\mathrm{Sb}_{5}\) as the optimal choice for a first target monolayer sample, although \(\mathrm{RbV}_{3}\mathrm{Sb}_{5}\) and \(\mathrm{CsV}_{3}\mathrm{Sb}_{5}\) samples are important comparative benchmarks.
