In this work, we introduce subset selection strategies for signal reconstruction based on kernel methods, particularly for the case of kernel-ridge regression. Typically, these methods are employed for exploiting known prior information about the structure of the signal of interest. We use the mean squared error and a scalar function of the covariance matrix of the kernel regressors to establish metrics for the subset selection problem. Despite the NP-hard nature of the problem, we introduce efficient algorithms for finding approximate solutions for the proposed metrics. Finally, numerical experiments demonstrate the applicability of the proposed strategies.