I know when I don't start with a small canvas everything is harder, and when I work with a big canvas I see things that would look better if I started with a small canvas.
There is not a lot of detail with speed painting, but even when you want to do a lot of detail is is always better to start with a small canvas. What I mean by a small canvas is you start with any size. Then double click on the Magnifying glass, and that will show you 100%. Then you use the crop tool and cut what you see. That will be a small canvas.
If you want to check it for how well it works with the brushes then select a really large brush and and see if it covers the screen. That size is great for drawing a sky, and if the brush has a soft edge it will blend the sky from light to dark. A lot of blending is harder to make smooth if the canvas is larger than the biggest brush. Photoshop's biggest brush is 2500 pixels. If that canvas is larger than that then the brushes will not do enough.
Any time you want more pixels to work with you can make the image bigger, with image size. Anytime you need more canvas you can add what you need with canvas size. I think those settings are under Image.
Photoshop has enough brushes to do anything, and when you might want something else it is not hard to make your own brushes. Anything you download don't always work, because you need to have the same version of Photoshop for the brushes to work. It is not that important, because there are only a few types of brushes in tradition art, and Photoshop has a lot you will never use unless you are playing around.
Yeah, you might have a better time if you don't download some big confusing brush pack. It's much better to watch a good video on how to make brushes, then when you think of something you might need a brush for (like trim on clothing, repeating chains or texture-y goodness), make your own. One of my favorite brushes for getting crazy texture is one I made by taking a picture of my shower curtain and cropping out a funky steam splotch with the magic wand.
As for other tips, don't neglect to learn about the different blend modes for layers and realize that no matter how hideous your layers are individually, it's only the final picture that matters.
I don't speedpaint, but my regular canvas is either 1920x1080 (wallpaper) or 1000x1300. No reason to download any brushes. Maybe when you become more adept with digital painting but I've still not yet needed any other brushes than the basic ones.