We introduce the ProSGPV R package, which implements a variable selection algorithm based on second-generation p-values (SGPV) instead of traditional p-values. Most variable selection algorithms shrink point estimates to arrive at a sparse solution. In contrast, the ProSGPV algorithm accounts for the estimation uncertainty - via confidence intervals - in the selection process. This additional information leads to better inference and prediction performance in finite sample sizes. ProSGPV maintains good performance even in the high dimensional case where $p>n$, or when explanatory variables are highly correlated. Moreover, ProSGPV is a unifying algorithm that works with continuous, binary, count, and time-to-event outcomes. No cross-validation or iterative processes are needed and thus ProSGPV is very fast to compute. Visualization tools are available in this package for assessing the variable selection process. Here we present simulation studies and a real-world example to demonstrate ProSGPV's inference and prediction performance in relation to the current standards in variable selection procedures.