The possessive is often placed first as a way of stressing it: "That is OUR wine (not yours)".
If it's placed first in cases where it's clearly not meant to be stressed, then Aaron is right in saying that it may sound a bit old-fashioned. There are, however, cases where placing the possessive just sounds better or is easier to say, and also semi-set phrases where it's customary to place the possessive first regardless.
So, as you see, there are no strict rules governing the placement; only guidelines with plenty of wiggle room and exceptions.
Adjectives get modified based on the gender or quantity of the noun they affect. Since "vin" (wine) is masculine you use the masculine form of "vår" which is just "vår". If it were "hus" (neuter) then it would be "vårt hus". If it were "baller" (balls) then it would be "våre baller".
It is all explained in the first lesson on adjectives I'm pretty sure. Hope that helps.