At some point, we all wonder What props should I run? Well the answer is not as simple as one motor requires one prop, there are several variables involved. If you are someone that doesn't like to read about things, but needs to learn by doing, feel free to skip to the bottom.
First let's get familiar with the "lingo", if you're not already;
When you're looking at props you will see a few different variations in calling out specifications. For instance, 5X4X3 means it's a 5" prop, with a pitch of 4, and 3 blades. Another would be 5045T, which is a 5" prop, 4.5 pitch, and 3 blades (the T stands for Tri-Blade). Similarly, 3X3X4, would mean 3", pitch of 3, and 4 blades or Quads (which may use a Q). If there is only two numbers, like 5040, and nothing else it is probably a bi-blade or 2 blade.
One more notable difference is the tip of the prop. The tip can vary in a few common ways, a normal tip comes to a point one one side of the blade. A bull-nose prop has a flat tip, perpendicular to the prop. This creates more surface area for the prop to generate thrust, but degrades efficiency. Blunt nose is sort of in the middle, and there are other odd ones like Wing-Tipped.
That should give you a pretty good understanding, let's move on.
Now we have things to consider when choosing a prop. Props can drastically effect amp draw, which in turn effects flight time. On a similar note props can effect speed and other flying characteristics. A higher pitch prop will accelerate faster, a stiffer prop won't bend under harsh throttle, etc.
So let's start with size.
Most quadcopters are built to accommodate a specific size, and hence are often called out by their prop size. A '5" Quad' means it runs 5" props. If you have already built your quad, this has already been determined. So I'm going to assume you built a 5" quad, as it's the most common. The rules are very transferrable between sizes.
Next let's think about how many blades we want. Having more or less blades changes two things, surface area and weight. Weight is relatively unimportant for 4"+, most common motors hardly notice the difference. Going from a bi-blade to a tri-blade is adding another 50% surface area. This does not necessarily increase thrust by 50%, but definitely has a notable impact.
Three blades is probably just fine for most pilots and situations, letting pitch and tip decide how harsh the prop is. But for those that are being very cautious, or perhaps flying in extreme heat, bi blade may the prop for you.
On the other hand we have quad blade, most of which are a 40 pitch, which won't hurt to try, but have very unique attributes.
Now let's get to pitch and tip.
These both effect two things respectively, amp draw and speed. More amp draw, more speed, more likely to explode, less flight time. Finding a good balance, for you and your quad, can be relatively hard. But your first goals are; don't hurt your battery, don't hurt your electronics. Your ESC's will probably be fine, but some motors can be more sensitive. As for your battery, if you don't have a strong enough battery for a very harsh prop, it will probably puff. I'll go over batteries in another post, but for now just keep that in mind.
In my experience, pitch ranges from 3-5, 3 being Very low, low and 5 being Very high. Staying in the 4-4.5 range will yield good and relatively Safe results. 5 will not typically add much power compared to the extra amps it will draw.
Then we have the tip or nose to consider, a bull nose tip (or similar) will help give you an extra umph and take respective amp draw. Most quads can deal with it, but be cautious. Blunt nose has a similar effect.
Last but perhaps most important; material.
You'll find that some props have harder materials, some softer, some thicker and thinner. What you want to base a decision on is your flying situation. If you're just starting or practicing something, use a stiff prop that can be bent back like a heavy DAL prop.
If you're trying to take a video use a very well balanced prop, like an HQ prop.
My highest suggestion for beginners is a DAL 5045T V2, or RaceKraft 5045BN Tri.
Hope that helps, feel free to comment.