Use whatever way of authentication it makes sense on your project. If you have only one authentication credentials you can relay on it being stored by default on the .Renviron file.
I'm not sure which is the "monthly cap of tweets" you are referring, if you refer to "500,000 Tweets per month from the recent search and filtered stream endpoints", yes this cap is applied on streamed tweets. Please, read in detail the documentation of the Twitter API.