Applying causal inference methods, such as weighting and matching methods, to a survey sampled population requires properly incorporating the survey weights and design to obtain effect estimates that are representative of the target population and correct standard errors (SEs). With a simulation study, we compared various approaches for incorporating the survey weights and design into weighting and matching-based causal inference methods. When the models were correctly specified, most approaches performed well. However, when a variable was treated as an unmeasured confounder and the survey weights were constructed to depend on this variable, only the matching methods that used the survey weights in causal estimation and as a covariate in matching continued to perform well. If unmeasured confounders are potentially associated with the survey sample design, we recommend that investigators include the survey weights as a covariate in matching, in addition to incorporating them in causal effect estimation. Finally, we applied the various approaches to the Hispanic Community Health Study/Study of Latinos (HCHS/SOL) and found that insomnia has a causal association with both mild cognitive impairment (MCI) and incident hypertension 6-7 years later in the US Hispanic/Latino population.