Traditionally a price factor, but not anymore.
The idea that you should shoot only black and white as a beginning "serious" photographer is both highly subjective and highly restrictive, especially in a world where colour comes at no cost. If you are shooting film and doing your own darkroom work, then there is a distinct price advantage to shooting in black and white; a beginning photographer in my day could easily have shot more than five times as many pictures for the same money (it becomes easy to see which negatives not to bother with), so you'd certainly get more practice in, but that's not really an issue in the digital world.
Abstraction in both monochrome and colour.
Black and white photography will abstract away one component of the image — colour — which will allow you to pay slightly more attention to all that remains. However all that remains is still an awful lot to consider when taking a picture. You're not "stuck" with tonal representations in black and white, and nobody has been since the advent of panchromatic films. With film, you can use filters to adjust the tonal relationships between colours; with digital you have even greater control.
You can have the same kind of abstraction in colour photography by shooting "flat" subjects (things that don't have much in the way of highlights and shadows) but have a lot of colour contrast to work with. In both cases, you are throwing out one thing that could have been part of the picture in order to make it easier for you to see other things.
Using digital tools to explore the photograph.
With digital photography, or at least with digital processing sitting in the middle of the photographic process, you can actually go a lot further. You can choose to look at your photographs in black and white, either just as desaturated images, or with special emphasis placed on certain colours in the image. You can choose to look at your photographs as just splotches of colour with most or all of the darkness/lightness information removed. You can "posterize" them, or look just for prominent edges and line. You can reduce them considerably in size (to about the size of a postage stamp) to force you to see the forest rather than the trees. You can blur them enough to see whether or not the picture holds together when you're not so distracted by what it's a picture of. You can flop the picture horizontally to see if it still makes sense (or has the same apparent problems, just in the other direction). You can view it as a negative, or solarize it, to help you see things that are hard to see when viewing the image "straight".
Things to bear in mind as a beginner.
There are good reasons for picking one means of seeing, like black and white, and sticking with it for a while. If you can get from overwhelmed to merely completely whelmed while learning, that's almost always a good thing. But that one means of seeing doesn't have to be black and white, nor does it have to be obvious in your finished pictures. Although black and white final pictures are likely to go over a whole lot better with an audience than hue-only or saturation-only pictures for example.
Using other visual media to study the art of photography.
All of that said, drawing can be an invaluable teaching tool for a photographer. I don't mean that getting good at drawing will improve your photography (although that can be true as well), I mean that taking a few hours to explore on paper how things like shading will affect your perception of simple shapes, and how much "knowing what's there" influences what you see. A couple of weekends (or a few evenings) spent with Betty Edwards' Drawing on the Right Side of the Brain (it's been out forever and can be found at any decent library) make a huge difference in how you see things, even if you never get to the point that you can actually draw anything that's even the slightest bit recognizable. It's mostly about getting past seeing what you know and starting to see what you see. Whether or not you can force your hand to replicate that masterfully on paper with a pencil is almost beside the point; the key is in losing your internal iconic representation of things so that you can see what's actually in front of you. And it will help a lot in post-processing, where the object of the game isn't really to show the viewer what you saw objectively, but to convey your subjective experience when you took the picture. Reality is often disappointing. Don't pay too much attention to the left-brain/right-brain theory stuff; the conceptual approach to drawing and seeing still applies even if the physiological assumptions behind it has been largely debunked.