One possibility is to use the option GridLines:
Plot[{f[x], f[1], f[2]}, {x, 0, 3}, PlotRange -> {{0, 5}},
PlotLegends -> "Expressions", GridLines -> {{1, 2}, None}]
or simply:
Plot[f[x], {x, 0, 3}, PlotRange -> {{0, 5}}, GridLines -> Transpose[{#, f[#]} & /@ {1, 2}]]
