Herein lies a tale that might help you decide whether you should trust your computer to your home television screen or to a specially-designed computer video monitor.

When I bought my Apple II Plus a year ago, I decided to hook it up to the color TV rather than buy a monitor. It would be stupid to do anything else, I reasoned, since such a setup would save me money -- not an inconsiderable consideration when the total outlay was expected to be in the $2,000-range.

The most obvious advantage -- aside from the $100 to $900 I saved by not buying a special monitor -- was that we'd be able to enjoy the color graphics that computer games employ without the expense of a color monitor.

But it didn't take me long to discover that there were serious flaws in the setup. Right off the bat, it became apparent that it resulted in the television being held hostage by the computer -- or rather by whoever happened to be operating it at the moment. No one else could watch any television programing in color as long as the computer was in operation.

We solved that problem by hooking up the computer to the family's tiny black-and-white set and hoped that that would be the end of it.

Yet, after a few days that too proved unsatisfactory. The screen of the black-and-white was not only too small for what we were trying to use it for, but its resolution was poor and the black-and-white contrast too hard on the eyes.

And what was it we were trying to use the computer for? Work-related tasks -- in my case, word processing. And as I was about to learn, that goes a lot easier with a particular kind of specially designed, computer-compatible screen.

Television sets are nice enough for watching fickle images from the airwaves, playing home computer games, and handling light word processing and programming tasks. But for really concentrated work on a computer, you'd be better served by a monitor especially designed for the job at hand.

In my case, a monitor with a green phosphorus screen is best. You've probably seen one: they crop up in offices where there's lots of word processing going on, like banks and lawyers' offices.

They are preferred because letters and numbers appear on the screen crisply, and the green is less tiresome on the eyes. Many programmers use them for these same reasons.

They also are relatively inexpensive, ranging from about $100 to $300, depending on how sharp you want the characters. Mine, a Zenith 12-inch model, cost about $130.

Many programmers prefer to use a composite video monitoring system. It provides full black-and-white resolution capabilities -- far better than the 30-to-40 characters per screen width that you get with a regular television -- plus some color, too, though the color is more like that you get on your television than what you can obtain with a color monitor designed for a computer. Composite units run from about $200 to $400.

If you want to blow the whole wad -- from $300 minimum up to as much as $900 -- you can get an RGB monitor. RGB stands for red, green, blue, and reminds you that with one of these monitors, your computer will feed the basic color signals directly onto the monitor's screen. Accordingly, these are what are known as "direct drive" units and deliver the highest color resolution and saturation possible, well beyond the meager capabilities of any home color TV. But a word to the wise spendthrifts who are intrigued: before you buy one, make sure your computer can work with it.

The moral is simple. If you're buying a home computer to use just for fun and a little half-serious work, then the old tube at home -- black-and-white and color -- will do just fine. You can always buy a specialized monitor later.