The question is why you would need to learn just any Slavic language? Generally, people have a reason they want to learn the language.
But if any language will do without regard to usefulness, then I'd recommend starting with a language written in Latin alphabet. In that case, I think Slovak may be slightly more approachable than the others. Both because of the its orthography and phonology. It also has slightly more regular morphology.
Of the languages that use Cyrillic, you may want to consider Bulgarian - purely because of its limited case morphology, which might make it easier to start. But for this very reason Bulgarian will be less useful as a foundation for learning another Slavic language.
Ultimately, if you want learn any language well, you'll have to put in about the same amount of work, so it does not matter all that much which Slavic language you pick.
The key commonalities among Slavic languages are:
- Complex inflectional case system
- Verbal aspect
- Cognates in the vocabulary
If you master any Slavic language (except maybe Bulgarian), you will have a really good foundation for learning the next one. But as a Czech native speaker who had to learn Russian, I can confirm that it will still take a lot of work.
The other thing to consider is how easy it is for you to get the right tools for learning (textbooks, dictionaries, software, videos) and opportunities to practice what you've learned. In that case, you may want to look around you to see, if there happen to be a lot of speakers of a particular language near to where you live. Russian and Polish are the most globally distributed and have the most online resources. But other languages may give you more local opportunities for practice.
You should also look into the availability of summer schools for your language. Attending these will be essential to gaining proficiency. So if you find one that is available in a time and place convenient to you, that may determine the language you start with.
Update on orthography:
Since most of the other answers focus on question of orthography, I've left it out of my answer. But perhaps it is worth noting that all Slavonic languages have orthographies that are relatively transparent in both directions (i.e. spelling can be predicted from pronunciation and vice versa).
For a beginner, Polish might present some visual difficulties due to its use of digraphs to represent single sounds but the relationship is mostly regular.
Russian presents more of a difficulty because the pronunciation of some vowels depends on lexical stress which is only marked in textbooks but not in normal writing.
South Slavic languages mostly have very transparent orthographies but Slovene does not distinguish certain phonological distinctions in vowels in its alphabet.
But in general, the orthography doesn't make much of a difference in making one Slavic language easier to learn than another. And certainly any similarities/differences will be almost irrelevant when moving from learning one to learning another.