Maybe the following resources can be helpful?
Reaction time distributions: an interactive overview https://lindeloev.shinyapps.io/shiny-rt/
I would usually not use a normal distribution for reaction times, because a) RTs cannot be negative, b) RT distributions tend to be right skewed. Both lognormal and shifted lognormal distributions seem generally good choices.
Another neat feature of lognormal and shifted-lognormal distributions is that the spread automatically scales with the size of the location parameter: ‘On the linear relation between the mean and the standard deviation of a response time distribution’ APA PsycNet)https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjywbrI6YDwAhV9hv0HHSsMCMYQFjACegQIBBAF&url=http%3A%2F%2Fejwagenmakers.com%2F2007%2FWagenmakersBrown2007.pdf&usg=AOvVaw1U0Odl5dNke2qaN71uGpJD
On why you might want to add a shift:
Are unshifted distributional models appropriate for response time? https://link.springer.com/article/10.1007%2Fs11336-005-1297-7 [paywalled, let me know if you have trouble finding access elsewere]
However, the shifted-lognormal model can be very sensitive to your lowest data points, which may lead to problems using loo (see e.g. this post: Error using Loo with moment matching)
But of course it always depends on your specific data and questions.