It isn't necessary to be familiar with many herbs to start using herbs for your health and the health of your family. Begin familiarizing yourself with one or two herbs. Use them on a regular basis. Get to know them and pay attention to their effect on your body. Once you become confident with those herbs you can gradually add one or two more at a time until you have several herbs you are comfortable using. As I have heard many times from various herbalists, it is better to know a few herbs well than to know many herbs superficially.
It is also helpful to focus on simple preparations rather than complex ones, especially when you are beginning your journey with herbs. In general the further a herbal preparation is from the herb's natural state, the more likely it is to have harmful side effects. Teas (also called tisanes) and infusions (basically the same as a tea but usually a stronger brew) are very simple ways to introduce herbs into your life. When someone in my family has a stomach bug, a headache or a cold, I usually turn to simple tea blends of three or four herbs and they are surprisingly effective. Herbal vinegars are another gentle way to introduce yourself to nourishing herbs such as dandelion. Don't forget you can also use some herbs such as chickweed and lambsquarters as vitamin-rich additions to the meals you prepare.
Sometimes people believe a herb has to be dangerously potent in order for it to work. I haven't found this to be the case. Some of the gentlest herbs I know are the ones I turn to time and again because of their ability to support various body functions and systems gently and effectively. When choosing a herb I prefer to use the gentlest herb possible for the situation. Sometimes it can be necessary to bring in stronger herbs but this isn't as common as one might think. My favorite herbs are tea herbs like chamomile and spearmint and culinary herbs such as garlic and thyme. (Okay, garlic is quite potent from a olfactory and taste point of view but it's not what one would consider a dangerous herb.) These herbs have been used safely for hundreds, even thousands, of years. That's not to say that some people aren't allergic to them but no more than some people are allergic to bananas or chocolate. It is, however, a good idea to take only a small amount the first time you try a new herb and pay attention to how it affects your body before drinking it in larger amounts.
This section could also be called "Start Fresh." It is very important that a herb be as fresh and vital as possible. A herb that has been carelessly picked and dried, pulverized, stuffed into bleached paper bags sealed with toxic glue and allowed to sit on a shelf for months is just not going to be as effective as a herb that has been carefully gathered in its prime, dried in good conditions, stored carefully and used within a reasonable length of time. One of the benefits of gathering herbs yourself is you can make sure you gather high quality herbs, dry them gently and store them properly. If you use them fresh in salads or stews you don't even have to worry about drying and storing them properly. If you are uncomfortable gathering your own herbs, you don't have anywhere to gather or you need a herb and you can't find it, you can buy herbs from reputable sources such as Mountain Rose Herbs.
Another reason to use local herbs is that they have adapted to the climate you live in and while some may argue against it, I believe they are especially suited to the various illnesses common to that climate. While exotic herbs often gain greater recognition and popularity you may be surprised to find that the very best herbs for you may be in your own backyard.