As a Russian I can assure you that nobody really speak Ukrainian, Byelorussian in those countries. Even considering hostility of Ukrainian nationalists to Russia that we have nowadays - really nobody speaks so-called 'mova' (Ukrainian language). Even Ukrainian fascist soldiers that genocide Russian in newly-formed Donetsk and Luhansk republics, mostly speak Russian and seldom Ukrainian on their videos available on Youtube. They do speak with slight accent typical for southern regions of Russia, but words and sentences building patterns are Russian, not Ukrainian.
I have noticed that even newscasters on Ukrainian TV who stick to anti-russian point of view, of course, do speak Ukrainian, but noticeably reluctantly, as if they translate in mind that they are speaking about. Absolutely the same thing is with Byelorussia (where I was born BTW, but I absolutely do not know Byelorussian and have never known).
These national languages are indeed used in deep provinces and villages where local people really speak them and are seldom spoken in the big cities. It is not relevant only for abroad countries. For example, my grandma-in-law has lived almost all her life in the village of Rostov suburb (not far from Ukraine border, but it has always been Russian area) speaks almost pure Ukrainian, and pronounces most of the words in Ukrainian manner. And other people from that village do so. Despite it has never been under Ukrainian government - neither in Soviet times, nor after.
Another thing is with Moslem post-Soviet countries - like Tadjikistan, Uzbekistan etc. Even in Soviet times they poorly spoke Russian and speak fluently only their native languages. Nowadays in these countries, as I suppose, Russian is almost forgotten, but for the foreign tourist it is preferable to speak Russian anyway. Some of people still know it, but almost nobody speaks English throughout all post-Soviet space.
For Georgia, Baltic countries (Estonia, Lithuania and Latvia) - i.e. for the post-soviet countries hostile to Russia, the whole thing is more similar to Ukraine rather than to Tadjikistan. I.e. formally they pretend to be non-Russian and pretend that they do not speak it, and Russian is officially prohibited, but indeed all of them are able to speak it. Since English knowledge is very poor among all post-soviet space and maybe 1% of people can make two English words with, do not expect to be understood. Maybe in large cities like Moscow and St Petersburg it is slightly better, and it will turn to be 2% instead of 1 )))
So... if you are going to travel to post-Soviet countries and going to study local language, Russian is the best choice. But do not delude yourself - most probably your pronunciation will not be understood by locals. As like as my English will seem clumsy to you )))