3D printer and design software for creating propellers for a toy airplane/drone I would like to begin designing and 3D printing propellers for both a toy airplane and drone that I own. I want to do this for experimental purposes.

I have never used a 3D printer nor have I used any 3D printing design software. So as a beginner to both of these things, I would like to know what would be the best type of 3D printer to use to create propellers for toy aircraft and I would like to know what is currently regarded as the easiest-to-use 3D design software for creating objects such as airfoils.

Also, at this time, the most I want to pay for a 3D printer is $500.
First, welcome to 3D Printing SE.  This is a great place to ask questions and get answers from people who have walked the same path.  I see from your profile that you are not a stranger to StackExchange and the available sites.

This question may be too broad for this SE Group, as it is asking for opinions rather than facts.  We try not to ask questions about "what is the best printer", or "what software is the best".  We avoid it both because it will change frequently, and because the answer needs to be gauged in your context, not the answerer's. We have some tools and community guidelines that suggest how to formulate the best questions.

Never-the-less, it is very hard when starting to even know how to make the first step, so with the indulgence of the group and your patience, I will make a suggestion or two.  These come from my experience and your's is surely different.

To try out 3D printers you may have resources the don't require buying one yourself.  It doesn't seem that 3D printing is the end goal for you.  You want to use 3D printing as a way to manufacture several experiments.  To access a 3D printer, it could be productive to check for local makerspaces, public libraries, or high schools with 3D printing capability.  You may find a friend you 3D prints who would be happy to run some objects for you.  You might even find it cost-effective to send designs to a service bureau such as 3D Hubs.  Note: I have no relationship with the company, although I did use their services once.

With the printing side temporarily in abeyance, you can focus attention on the design side.

If you are familiar with programming, you might be able to use either OpenSCAD or SolidPython as a design tool.  If you want something graphical, it might be worth trying OnShape.  NOTE: I know at least one of the founders of OnShape, but have no investment nor role in the company.  There are many design tools available.  For designing technical parts, I think you want tools more focused on technical than aesthetic content.  

I would avoid purchasing a printer unless you want 3D printing and 3D printers to be part of your project.  People have mixed stories with many brands of printer, and lower-cost printers often become projects in themselves.  They can be satisfying, rewarding, and learning-driven projects, but can distract you from your prime intention for a long time.  In my case, I wanted to print boxes for projects, and prototypes for larger wood carvings.  I designed a printer, acquired materials, built it, and spent 3 years playing with it.  Along the way, I made some useful prints.  Eventually I was tired of not having a reliable 3D printer, and I wanted to reliably make things.  I needed a printing appliance.  So I bought a mid-range printer (which works very well for me), and I don't mess with it (much).

So, a broad answer in response to a broad question.  Welcome to 3D printing, the hobby and the StackExchange site.