Hi Brandon,
About your questions:
- How you call the subdirectories shouldn't be a matter: /es/ or /es-es/ (it's meant to be descriptive and short for users but non-relevant at this point as a signal towards search engines). However, what's important is how you name the URLs of each language version later: they should be in the language of the content that they show.
- If your international versions are country targeted (meant to be focused on users in a specific country and not language targeted, meant to focus on any user speaking a language) then you should geolocate them through Google Webmaster Tools.
- You should also use hreflang annotation in your different pages, referring to each URL language (and country, if they're geotargeted) too, so you won't end-up facing any content duplication issues, since you might have for example a Spanish version targeting to Mexico with a very similar Spanish copy than your Spain version. If you add the annotations then Google will know these different URLs are targeting to different countries or languages audience and shouldn't cause a content duplication problem.
- If you can't just translate/localize the whole site structure to other languages, then it's a must that you prioritize. Start with those language / countries that have the higher current audience for your site and have the higher potential to grow too. Enable just the most important landing pages / sections of your site if you can't do them all, the ones that you can really maintain, translate / localize well, to give also the best user experience to those visitors (besides of being able to rank with them well in search engines).
Take a look at this post where I wrote about how to set an International SEO strategy well from the start and avoid running into issues in the implementation later.
Thanks!
Aleyda