As a WP developer, most of the premium themes you find around (on themeforest) for instance, follows basic seo guidelines So mostly, saying the theme is SEO-optimized is a marketing act. I would advise you to,
- Get a theme that looks good to your audience.
- Nearly all themes are mobile responsive right now so I don't even bother to tell you to check it
- Check what people are saying about breadcrumbs and tags. I mostly don't use either.
- Yoast SEO is a cool plugin, use it.
- Depending on your site, you can choose to disable author and/or date archives. For example if you only have 1 writer on the site, author archives are just duplicate content that is not good to anyone.
- Get a decent hosting. Loading times do matter and contrary to what some people think, slow loading times occur cause of cheap-ass $1 for 10 years hosting instead of poor theme coding.
- Optimize your images. You can use RIOT for it, has the bulk optimize tool. I think it is much better than using WP Smush or any other wordpress plugin.
- Caching. Check G's pagespeed insights and see if it states a problem with caching. W3 Total Cache usually does all the trick, Leverage Cache Browser Ninja's does the remaining if you don't want to bother with manual .htaccess edits.
So, I know that you stated a theme to provide all for you but that is kinda non-existent. For me, the theme is just for bounce rate.
