We investigate properties of carbon-oxygen white dwarfs with respect to the composite uncertainties in the reaction rates using the stellar evolution toolkit, Modules for Experiments in Stellar Astrophysics (MESA) and the probability density functions in the reaction rate library STARLIB. These are the first Monte Carlo stellar evolution studies that use complete stellar models. Focusing on 3 M$_{odot}$ models evolved from the pre main-sequence to the first thermal pulse, we survey the remnant core mass, composition, and structure properties as a function of 26 STARLIB reaction rates covering hydrogen and helium burning using a Principal Component Analysis and Spearman Rank-Order Correlation. Relative to the arithmetic mean value, we find the width of the 95% confidence interval to be $Delta M_{{rm 1TP}}$ $approx$ 0.019 M$_{odot}$ for the core mass at the first thermal pulse, $Delta$$t_{rm{1TP}}$ $approx$ 12.50 Myr for the age, $Delta log(T_{{rm c}}/{rm K}) approx$ 0.013 for the central temperature, $Delta log(rho_{{rm c}}/{rm g cm}^{-3}) approx$ 0.060 for the central density, $Delta Y_{rm{e,c}} approx$ 2.6$times$10$^{-5}$ for the central electron fraction, $Delta X_{rm c}(^{22}rm{Ne}) approx$ 5.8$times$10$^{-4}$, $Delta X_{rm c}(^{12}rm{C}) approx$ 0.392, and $Delta X_{rm c}(^{16}rm{O}) approx$ 0.392. Uncertainties in the experimental $^{12}$C($alpha,gamma)^{16}rm{O}$, triple-$alpha$, and $^{14}$N($p,gamma)^{15}rm{O}$ reaction rates dominate these variations. We also consider a grid of 1 to 6 M$_{odot}$ models evolved from the pre main-sequence to the final white dwarf to probe the sensitivity of the initial-final mass relation to experimental uncertainties in the hydrogen and helium reaction rates.
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