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...frame size, like "fit" is a personal choice, and depends a lot on your needs and expectations for use.
Yes, you have a number or choices in adjusting your saddle to bar distance, including longer and shorter stems. Yes, having longer arms does factor in, as does your personal preference on what "feels good" to you on the bike.
You're in the road forum, so you can expect to get some advice on what would be the best choice if you were anticipating some Cat 5 road racing endeavors. Similarly, guys who ride cross bikes will give you different ideas.
In general, if you can make the standover on your chosen bicycle, you can usually get it fitted to something you will enjoy riding unless you are one of the poor souls with an exceptional anatomy. Getting comfortable on any bike new to you is a process. Good luck with it.