Recently, I have been interested in creating my first campaign setting, but knowing where to start has been more difficult than I thought. I have a few ideas on what I want to make, but I'm not sure if I should start creating the "big picture" of the setting or starting small. What are some some good ways to start?

Speaking as someone who tried this before, writing a campaign setting is like writing the world of a fantasy book. Only write the things you need for the first few sessions, then expand from there. Will the players enter a town? Make that town. Will they need to talk to an NPC to continue the story? Put more effort into that guy than others. If you try to write a whole world in one sitting, you'll get burned out. Its like render distance in video games. The farther away from the players an object or place is, the less effort you should put into writing about it. If they start migrating in that direction, add more detail by the time they get there. 

Definitely have to agree, only make the things you need. If you want to come up with cities, I"d come up with the basics. Like size, location, maybe a sentence describing it.

I would suggest that you start small. One town, a dozen or so NPCs and a few key locations (tavern, shop, Smith, trader's hall, market). From there you can either do a quest board style system for the adventure, or have a multi-part objective.

I would also suggest reading through Dragon of Icespire Peak and Lost Mine of Phandelver. You'd be looking specifically for how it creates the town, the people, and the quests in and around the town. It's a good model for creating something similar.

Come up with a start and an end and some points of interest that you want to add into the campaign but be willing to change that. Don't wright stuff that will happen 4 sessions from current session. To quote a wise man "all good adventures start in a tavern" throw all the PCs in a tavern or some other social place if a tavern wouldn't match the vibe of the story, and let them RP for a bit even if it's not a RP centered campaign, it helps the players get into the shoes of their PCs and lets them know the world that they're in better as well as any other PCs they meet, having one event to tie all the PCs together, and get them working on a common goal. Also, if you're entirely new feel free to ban evil or chaotic characters as they can and will mess with the plot and test, your abilities as a DM.  All around know your place, you are not an enemy of the PCs you are simply the one that describes the world around them, the world you built, in other words, let the dice be their enemy not you.

One good rule of thumb is to make one location, along with anything which they could get to in 1-2 session around it. So it might be a druid circle in the forest, along with all the interesting stuff around it. Until they leave the forest, don't even worry about where the forest is or what's around it!

Best step I took for this is to ask the players, at the end of every session, "Where are you going next". Vastly helps me to prepare content in the correct direction!

Most of these suggestions are pretty spot on. I will add these items:

While someone suggested starting with just your immediate adventuring area (GOOD advice), give thought to the size and climate of your continent (the world can come later, but you can keep the entire campaign on a single continent and fill in others and islands and build the world much later)

Is the entire continent one country? many nations?  What's the general alignment? Are the people and politics generally good? Or is it ruled by an evil despot? Is slavery legal? How high tech is it? is there yet gunpowder? canon on ships? muskets or pistols? Are there steam engines? Or would even an artificer profession be too high tech? is magic rare? Or fairly common? (will they find a +1 weapon at level 3, or not until level 9? or never!?)

Will the politics be a Medieval monarchy? A Roman emperor with Republic-style senate? democracy? no political structure at all? (maybe the last king died with no heir and now there is anarchy)

Religion: Will you create your own pantheon or borrow from the rules and source books? Or will you use greco-roman or norse mythology? or are there multiple pantheons co-existing, or variable by country? Is there just one god? Are there no gods at all?

Trade: Is the nation self sufficient? do they trade with neighboring kingdoms? Is trade with foreign places facilitated by shipping? What is industry like in your starting zone? farmers? a mining area? hunting and skinning? fishing and ship building? are the farms mostly for grain, or are there orchards of fruit? flax for linens and textiles?

Obviously, you don't have to have detailed answers to all of these questions at game one (and your energies would be better used elsewhere). But you should start formulating ideas of how you want to steer things. These are things you can thing about while commuting to work or school, on your breaks, walking the dog, in the shower. Any time your mind isn't needed to be focused on more important things.

If characters want more info about the world, don't tell them as the DM (especially if you don't know). Have them RP asking NPC's (who may not be authorities, and may give answers that you change later...and then say "I never told you that, it was Jake the one-eyed fisherman who told you that")

I am on my sixth or seventh campaign setting (I started in 1979), and it is not fully fleshed out.  a few entire continents on my world map have not even been started after 4 years of use, and likely won't be until I have need for them.  But they exist for flavor and scope...for now.

World building is a ton of fun.  You may find yourself enjoying very specific parts and spend many hours on it while virtually ignoring other things. That's fine.  Do what you enjoy.  If you feel pressured into a completionist mindset, you may burn yourself out and turn this from a fun chapter in your gaming career, to a frustrating chore.

I wish you luck!  It's a labor of love.  have fun!

Not that I disagree with the above advice, its all fair and good, but its not how I do it.  Mind you this is me sharing my personal preference rather than offering advice, but maybe it will inspire you.

Basically I look at setting creation from the perspective of a "Chronicle".  When I start, I usually initially create a basic map using a tool like Inkarnate, just an outline of a continent or area, depending on how big or small I want to start.  I don't fill in the map, I just sort of do an outline.

Next I start writing the story of a very specific part of the world, for example in my current chronicle I decided to start with an area and describe how Dragonborn came to live their.  Where did they come from for example?  I decided that they were created by Elves as a sort of "cattle" to be raised and slaughter for their parts which have magical properties.  Now just from that basic outline, I had the makings of a story that I could write.  Why did the Elves create them?  What are the magical properties and what are they used for?  From that I get answers about the world like an explanation where magic items come from.  Etc..

Anywho I keep writing the chronicle in this way until I have enough background material to create a campaign and I put together a hook to the story and the campaign becomes the first part fo the history of my setting.  My players actions in the story will determine what happens in the world over the next generation.  When the campaign is over, I write the second chronicle, incorporating everything created for the first, as well as the history created by the players and I start expanding on the setting.

Usually after 3-4 Chronicles I have a fully functioning setting and the advantage of doing it this way is that my players grow up with the setting.  They learn about it piece by piece and they become involved in creating parts of its history.  This creates a personal attachment to my setting and the end result is sort of a shared setting we create together.  I don't want to just post one of my Chronicles because sometimes these Chronicles I turn into published material later or they become part of something I publish, but I sent you a link (OP) to the chronicle so you could check out what I mean.

My personal opinion is just go as big or small as you want. I started with a basic realm (Faerun) and then made it a small part of my custom world. Then I started making a whole history and Everthing! Really do what you want and what works for you

My preference is to lay out the portion of the world I intend the campaign to take place in in large strokes. I started with the ideas of what kind of cultures I wanted to include then drew a map that supported those cultures, but you could also do it the reverse with drawing a map then using the geography to determine regional cultures. For instance, I decided I wanted the Fey to be an isolated culture on the Material plane so I drew a region surrounded by mountains (like mordor) for them to inhabit, in addition I wanted a more technological mercantile culture so they became a coastal nation dominated by a large river  connecting them to the inland nations. Then I added a viking/mongol-esque culture who got a rugged less fertile northern region next to an ice sheet that defined one edge of the campaign area. And a warring-kingdoms nation in the middle to tie it all together, and some fiercely independent dwarven city-states in the mountains around the Fey.

Next I came up with a major threat on conflict for each region - Fey were on the brink of civil war between the Seelie and Unseelie, the north was threatened by an ice-sorcerer-queen and her cult, the merchants were having their ships attacked by an Aboleth and it's army of corrupted merfolk (using the Merrow statblocks) and it's mindcontrolled kraken, the warring-kingdoms were suffering a famine as their king had been usurped by a dark wizard, and the dwarven city-states were under threat from a dragon that had recently moved into the mountains and was demanding tribute from them.

I drew the map and put on a few major cities, and let the players choose where they wanted to come from and where they wanted the campaign to start and then filled in the details as they decided where they wanted to go and what they wanted to do.