If you have turned on the new language subsetting feature, the options in your kit editor will be different. Read more about subsetting and how to opt in to early access in this blog post.
Many fonts on Typekit support Russian. You can browse fonts that support Russian by selecting "Russian" from the list of supported languages in the sidebar under browse fonts.
In order to serve fonts in Russian, you must enable the "all characters" set in your kit. All fonts that support Russian include (at minimum) the following letter characters: