How many observations (n) and dimensions (d) are you particularly studying?
Probably you are in the n>>d case, but more recently d>>n is a hot topic.
Variable selection is something that needs to be done before-hand. Check for feature correlation, this can affect the number of clusters that you detect. If the features are correlated and they happen to be linear, you can use the gradient instead of the two variables.
There is no absolute answer to your question. Many methods exist because of this. Clustering is explorative by nature. The better you know your data the better you can design tests.
Need to define what you want to test: stability of the partition, or, the stability of the clustering recipe. There are different ways to deal with each of these problems. For the first one, resampling is a key, and, for the second one, the use of comparison indexes to measure how many observations were left out of certain partition is often used.
Recommended reading:
[1]Meila, M. (2016). Criteria for Comparing Clusterings. Handbook of Cluster Analysis. C. Hennig, M. Meila, F. Murtagh and R. Rocci: 619-635.
[2]Leisch, F. (2016). Resampling Methods for Exploring Cluster Stability. Handbook of Cluster Analysis. C. Hennig, M. Meila, F. Murtagh and R. Rocci: 637-652.