An alternative approach is the Exploratory Data Analysis route. Perform all the initial steps like missing values treatment, outlier detection and removal, resolve multicollinearity or collinearity issues to obtained high variance features. These steps will help in both dimensionality reduction as well as feature selection. Thereafter, you can apply any of the heuristics like the Elbow method, or the Gap statistic method or the average silhouette method;
Elbow method - This method can be traced to Robert L. Thorndike in 1953. Essentially, a line is plotted on a graph and the bend in the line indicates a possible number of clusters. In R it can be done using the NBClust package.
Average silhouette method computes the average silhouette of observations for different values of k. The optimal number of clusters k is the one that maximizes the average silhouette over a range of possible values for k (Kaufman and Rousseeuw 1990).
The gap statistic compares the total within intra-cluster variation for different values of k with their expected values under the null reference distribution of the data. The estimate of the optimal clusters will be a value that maximizes the gap statistic (i.e, that yields the largest gap statistic). This means that the clustering structure is far away from the random uniform distribution of points.
The aforementioned heuristical approaches can help you determine the appropriate number of clusters. Once you have found the clusters, you can then study and label them thereafter you can do prediction