Noise in genetic networks has been the subject of extensive experimental and computational studies. However, very few of these studies have considered noise properties using mechanistic models that account for the discrete movement of ribosomes and RNA polymerases along their corresponding templates (mRNA and DNA). The large size of these systems, which scales with the number of genes, mRNA copies, codons per mRNA, and ribosomes, is responsible for some of the challenges. Additionally, one should be able to describe the dynamics of ribosome exchange between the free ribosome pool and those bound to mRNAs, as well as how mRNA species compete for ribosomes. We developed an efficient algorithm for stochastic simulations that addresses these issues and used it to study the contribution and trade-offs of noise to translation properties (rates, time delays, rate-limiting steps). The algorithm scales linearly with the number of mRNA copies, which allowed us to study the importance of genome-scale competition between mRNAs for the same ribosomes. We determined that noise is minimized under conditions maximizing the specific synthesis rate. Moreover, sensitivity analysis of the stochastic system revealed the importance of the elongation rate in the resultant noise, whereas the translation initiation rate constant was more closely related to the average protein synthesis rate. We observed significant differences between our results and the noise properties of the most commonly used translation models. Overall, our studies demonstrate that the use of full mechanistic models is essential for the study of noise in translation and transcription.