A while back I needed to teach some high school students how to design PCBs. After looking at various tools, I selected EasyEDA. There were two main drivers for this selection: 1) It is relatively easy to learn and use, and 2) it required only a browser and I didn't have to be concerned about installation and support on various computers. It turned out to be a good selection. The students were able to learn it quickly and it got the job done.
The tool I usually use is Kicad. The learning curve is a bit steeper, but it's a much more capable software package. If you intend to keep doing PCB design, you'll be better off with Kicad. As you do more complex designs, Kicad will continue to meet your needs. If you decide to use Kicad, I recommend that early on you spend some time learning how to create your own components and footprints. Then, over time, build up your own library.
When you have a design done, use the 3D viewer to see what it's going to look like. Then use the Plot icon to generate the gerber files. Use the gerber viewer to look at the results. When satisfied, put the gerbers in a zip file and send it to the fabricator. They'll do another check and let you know if they have the right files.
Here's another tip: use the OSH Park website to process and render your files. They'll generate an image of what your end result will look like if they make the boards. This way you can confirm that you sent good files that have everything the fabricator needs.
Another thing I've learned from experience is to not send the files the day you finish the design. Wait a day or two and then carefully review your work. It's always amazing how errors can become more obvious when you return to a design after being away from it for a while!