Don’t worry, I am here to help you figure it out as a beginner to 3d software.
Straight to the point: Yes you can export to mp4.
Within the Output section of the Output Propreties tab, you select FFmpeg video, and more options will appear below it. In Container, select the file format, which in your case is MPEG-4 (.mp4). You can then access some other settings there like the quality of the video and encoding.
To render, click the render animation button (or use the hotkey Ctrl+F12):
Each frame will be rendered out as specified in the timeline, and once all the frames are rendered, the video is saved to your computer, wherever you specify it to be saved set within the Output section (first image above).
The below goes into detail about the second option you were confused about. You don’t have to do it if you don’t want. The first option is definitely quite straightforward.
Now, what I was saying that confused you a bit was the alternate rendering method. Essentially, when rendering an animation, each frame is calculated and rendered out, one-by-one until they are all done. If you instead selected an image output instead of a video output, each frame will be rendered and saved as an image to your computer, like below:
Here you can see many frames I made for a short Mars animation rendered out as images.
One benefit to this is that each frame, once rendered, is directly saved to your computer. A video on the other hand does not save until it is finished rendering the entire animation timeline or until it is cancelled. Having individual frames gives you a bit of security in data, as if Blender or your computer was to suddenly crash, lose power, or fail in any way, all the rendered frames up until that point has already been saved and you will not lose them. A video, however, would not have such security. The frames are not saved and the video will only be saved once everything is complete. A failure would mean that none of the rendering that occurred was actually saved, and you would have to re-render everything again.
The other benefit is having high quality rendered frames, giving you much more freedom as compression would not be much of an issue. You could also use those rendered frames in other things, like still renders for some sort of thumbnail, art, etc.
Now, of course this option means that you have to go and combine all the frames into one video. It may be a bit of an issue in organisation, but it depends on the software. Some can handle it well. I have no experience with Final Cut Pro, so I cannot say for that, though.