Does Fairy Tail have one main goal / plot, or is it just many separate stories?
If you are asking whether or not Fairy Tail is episodic, it is very much not. Similar to other Shonen series, it is broken up into a number of story arcs, with the first few being shorter in length and the later ones being much longer.

If watching the anime, there are a lot of extra episodic filler segments scattered between arcs, but those are technically not canon.

In terms of arcs themselves, around Episode 10 more substantial arcs appear (story arcs of at least 10 episodes), starting with Galuna, Phantom Lord, and the Tower of Heaven. 

If there is a 'main plot', the first real introductory seeds (Dark Guids + Zeref, etc) are sown in the Oración Seis arc (according to the wiki, starts apx. Episode 52), but it's hard to pinpoint a 'main plot' until much later. There are more lighthearted arcs mixed in between the more serious arcs but generally speaking I'd consider things post-timeskip to be where things settle in on a main plot (albeit in a roundabout manner). 

From the Tartaros Arc (Ep. 234) onwards, it's pretty much the 'highest stakes' portion of the series.