THIS PAPER IS ELIGIBLE FOR THE STUDENT PAPER AWARD. DNA emerges as a promising medium for the exponential growth of digital data due to its density and durability. This study extends recent research by addressing the \emph{coverage depth problem} in practical scenarios, exploring optimal error-correcting code pairings with DNA storage systems to minimize coverage depth. Conducted within random access settings, the study provides theoretical analyses and experimental simulations to examine the expectation and probability distribution of samples needed for files recovery. Structured into sections covering definitions, analyses, lower bounds, and comparative evaluations of coding schemes, the paper unveils insights into effective coding schemes for optimizing DNA storage systems.