We discuss phenomenological aspects of inflationary models with a no-scale supergravity Kähler potential motivated by compactified string models, in which the inflaton may be identified either as a Kähler modulus or an untwisted matter field, focusing on models that make predictions for the scalar spectral index $n_s$ and the tensor-to-scalar ratio $r$ that are similar to the Starobinsky model. We discuss possible patterns of soft supersymmetry breaking, exhibiting examples of the pure no-scale type $m_0 = B_0 = A_0 = 0$, of the CMSSM type with universal $A_0$ and $m_0 \neq 0$ at a high scale, and of the mSUGRA type with $A_0 = B_0 + m_0$ boundary conditions at the high input scale. These may be combined with a non-trivial gauge kinetic function that generates gaugino masses $m_{1/2} \neq 0$, or one may have a pure gravity mediation scenario where trilinear terms and gaugino masses are generated through anomalies. We also discuss inflaton decays and reheating, showing possible decay channels for the inflaton when it is either an untwisted matter field or a Kähler modulus. Reheating is very efficient if a matter field inflaton is directly coupled to MSSM fields, and both candidates lead to sufficient reheating in the presence of a non-trivial gauge kinetic function.