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?
The DMG is much more important.
First, it's worth noting that it's pretty important to have all three books.
That being said, the DMG contains lots of useful information for a new DM. While more experienced DMs might scoff at the advice inside, there are still a lot of useful tables, maps, and suggestions in the DMG that are good for getting off the ground.
Additionally, the DMG contains the list of magic items, as well as guidelines for creating your own monsters and magic items. With the sample monsters in the PHB and the creation guidelines, you could create your own monsters fairly easily.
A lot of Monster Manual is (legally) available online.
The Open Gaming License legally makes a large list of monsters available for free. You can access this list at various places on the internet (here, for example). The list is missing some classic monsters, like the beholder, but for practical purposes it doesn't really matter.
On the other hand, a lot of the DMG advice and creation guidelines are not legally available on the internet (though many magic items are). Thus, buying the DMG gets you a lot more stuff you couldn't get otherwise.
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 and the SRD, 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).
If you must purchase one of the two, since you've indicated you're making your own campaign then I guess the choice would be DMG, given that you'll have plenty of SRD monsters to populate your world but the worldbuilding and campaign design bits of the DMG aren't freely-available. (Then again: the lore-parts of the MM that aren't SRD are pretty awesome and would stand in for a lot of world-building. Still, on "Encounter Design" and "Adventuring Day" and a few tables and sample maps I'd lean toward DMG, personally. If you had to choose one of those two.)
But you're not constrained to buy one of those two, there are lots of RPG products out there!
Buy the Starter Set. Or one of the hardcover adventures. (But the Starter Set's better.)
The Starter Set is designed specifically for you: it assumes a new GM and does a few nice things to help you along:
- presents the players a restricted set of options (drawing from the Basic Rules) so that you don't have to have twelve classes' features at the tip of your brain, just four;
- annotates the adventure with GMing sidebars relevant to the material at hand, pointing you to rules on hiding, or overland travel, or exploration, or social negotiations at times where they're likely to come up;
- fleshes out a scenario large enough for players to wander around and have some freedom in, but small enough to easily keep in your head.
Other benefits to you:
- there's a network effect: you'll find plenty of other new (and experienced!) GMs who've run the Starter Set and can share experience, vs. the zero other people who've run your custom adventure;
- it's got a natural endpoint: you don't run the risk of disliking a setting that your players love and feeling obligated to run it a year past your expiration date;
- using a written adventure allows you to pay more attention to the player-GM dynamic, to rules-questions, to spotlight management... all things that will, in time, become second nature but which will occupy more bandwidth in your early games.
Then seek out advice when problems arise.
Talk with your players. Talk with other GMs. Read gm-technique questions here. Browse forums. Read GMing blogs. Play in other GMs' games.
With actual quandaries in hand you'll get much more from these resources than you will reading--even memorizing--the DMG. Because the DMG, containing many good things (and hints), is as well laid out as almost any D&D (TSR or WotC) product: it's a great reference once you already know (basically) how to do the thing it purports to present.
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.