Question: This is my first time DMing, and I already have the Player's Handbook. I'm wondering which core book I should get next: the Dungeon Master's Guide or the Monster Manual? I am creating a campaign for four players, and I already have some of it done, but I would like to have better sources for the rest of the campaign. Which one is more useful?

Answer: 
I'd recommend getting the DMG first. You can create your own monsters (stat up natural animals, they're likely to be adequate for first level characters), stat up NPCs from playable races in the PHB, and save the "monster" stuff for later adventures. You will, however, certainly want the additional rules in the DMG; the PHB presents only the player-facing subset, and isn't in itself enough to run a game even if only PC races are present on both sides.

For monsters, between the [Basic Rules DMG](http://media.wizards.com/2016/downloads/DND/DMBasicRulesV05.pdf) and the [SRD](http://media.wizards.com/2016/downloads/DND/SRD-OGL_V5.1.pdf), both available at WoTC for download, most (but not all) of the monsters used in D&D are available. That inventory of monsters is enough to run a long campaign. (Some of the product identity monsters like Beholders and Illithids are only in the Monster Manual).
As a general rule I typically go PHB > GM Guide > Other stuff in that order. Mostly because the PHB and GM guides tend to compliment one another (your mileage may vary). Which is to say that the GM guide may refer to specific examples from the players guide or add additional clarifications to rules. On the other hand, books such as the Monsters Manual are more reference material for things that you can throw into your game.  

Additionally, I would also do a couple of web searches for GM tips (aka free advice). For the most part game mastering *can* be genericized to a point. Which is to say there are problems, and solutions, that all game masters have. Going into more specific problems can be asked with further questions here.