Oh, gosh, the usual Hindutva nonsense. Let me first of all dispel any notion that I don't like learning languages "for fun." See my Hacker News user profile for more details on what languages I have learned. I have learned enough facts about Sanskrit and the various languages that are written in the Devanagari alphabet to know
1) The written history of Sanskrit is much less that 3,000 years long. (The historiography of India is hard, because most of the writing materials used in ancient India were perishable, and thus much less preserved than the written records of other parts of the world that are equally old, but plainly the Vedas and other texts from ancient India are less than 3,000 years old.)
2) Yes, Sanskrit is an Indo-European language, which means it brings to mind features of other Indo-European languages. Each cognate language makes it easier to learn other cognate languages in turn. So you could gain an advantage in learning Sanskrit, for example, by learning German, Russian, and Greek first (as I have). Or you could learn Sanskrit first, as many secondary school students in India have done. But while learning each language, you might still ask yourself, "What texts am I going to read, or what conversations will I have, now that I know this language?" Sanskrit doesn't have a particularly high degree of utility, if that is what you are looking for in a new language, for day-by-day communication today.
3) Finnish is not an Indo-European language, so it is not cognate to Sanskrit, and therefore learning Sanskrit doesn't provide much advantage for learning Finnish. Come on, get the basis facts right. Learning Estonian would provide a huge boost for learning Finnish, of course. Learning Hungarian, Turkish, or even Mongolian would provide more remote advantages for learning Finnish.
4) Learning Tamil, Malayalam, or other languages of south India usually categorized as Dravidian (not cognate with Indo-European) languages just might give you a deeper understanding of India and its cultural heritage than the same effort spent learning Sanskrit. That's something to think about if you like India and its culture, as I do.
5) If you would like to learn a language that maps well in its linguistic structure to first-order logic notation, I strongly recommend Chinese (Modern Standard Chinese or some other Sinitic language) over any Indo-European language, including Sanskrit. All languages have arbitrary grammatical rules. Strictly speaking, no language is more "logical" than any other. But if you like a one-to-one correspondence between spoken language sentence structure and the usual first-order logic notation, Chinese is a good place to start.