Feature Selection

Feature selection aka model selection is difficult. By that I mean it is an unsolved problem and there is evidence that it is an NP-hard problem. The title of Maymin (2011) hints at why: "Markets are efficient if and only if P = NP." However, there are a few heuristic tools often used.

First, we rest on theory. If theory suggests a term should be in a model, we try it. If there is theoretical evidence that term matters, we may even keep it in the model despite it seeming to be insignificant. Statisticians refer to such a term as a nuisance parameter; economists often refer to these as controls or fixed effects -- though a nuisance parameter might not correspond to individuals or any group or time identification.

Next, we can try forward and backward selection: adding covariates from a base model or subtracting them from a kitchen sink model. This is common though it can lead to some problems.

We can also look at other evidence: which coefficients grow fastest as we relax the penalty in a LASSO or ridge regression. However, even this can lead us astray. Some people will throw support vector machines or other ML methods at the problem, however these can easily lead to overfitting and thus poor feature selection.

Feature/model selection is still very much an art.

Using Seasonally-Adjusted Data

If you are forecasting a year or a few years out, using the seasonally-adjusted data is likely to be OK. If you are forecasting within the year, however, using the seasonally-adjusted data has proven problematic. For one explanation how this can cause trouble, read Kroencke (2017) in the Journal of Finance. However, in brief: the seasonal adjustment reduces the noise too much which leads to spurious anomalies.

Future Values

As for how to get the future values... I am unsure what you mean. Are you looking for values of these indicators in the future, forecasts of these indicators, or macroeconomic information from futures markets?