There are lots of things that people get confused about when exploring witchcraft and Wicca. And there are lots of rather peculiar ideas that get expressed too which don't always make much sense when they are examined a bit more closely.
Just to give you some background on where I'm coming from: I've been actively practicing witchcraft for over twenty years now. I consider myself to be a Wiccan. There are poorly-educated Wiccans out there just like there are poorly-educated participants in any group that can be identified. And there are also plenty of well-educated people out there who know what they're talking about too so it's usually not wise to dismiss a group because of a preconception.
Witchcraft is basically folk-magick practices, in my opinion, which are not tied to any one religious system. You can be a witch and pretty much any religious persuasion, even atheist. The key to being a witch is that you practice some form of magick. While many witches do make magick an integral part of their religious practice it doesn't have to be a religious thing.
Wicca is a religion, first promoted widely (and very likely invented in its first real form) by Gerald Gardner. It's based on witchcraft practices but tries to draw from pagan religious practices for the spiritual basis. It is very much a product of its time and culture, though, so has a lot of obvious Golden Dawn, theosophical, Thelemic, and even Christian elements in it. And it's a constantly evolving thing with a lot of diversity in its expression today. But at its core, Wicca is a modern Pagan religion that incorporates witchcraft.
Witches are usually not as structured as other magickal practitioners such as ceremonial magickians. Most witches are very individual and idiosyncratic in what they do. They usually draw from a wide variety of sources and above all else use what they find works personally for them. If something doesn't work for them it is usually left by the wayside. But what works for me might not work for someone else. And what doesn't work for other witches might work very well for me.
There are different systems/sects called "traditions" which have become established in the Wiccan and larger witchcraft community. These groups usually have formally established ways of training and working, established rules, and established cycles and theology that they use. There are also many many eclectic Wiccans and witches out there which don't follow particular systems, and many many solitaries who don't belong to any formal groups at all.
The age of something doesn't necessarily determine whether that thing or idea is more useful or less useful to a witch or Wiccan. If it works for you then it works for you; it doesn't really matter if it was invented a hundred years ago, a thousand years ago, or yesterday.
There is a lot of talk about "traditional witchcraft" that goes around. It seems to be a way for people to try and give their ideas or practices a mystique, an aura of authority, by presenting it as being old. The one thing we know about how pre-Gardnerian witches and cunningfolk practiced is that they used what worked for them, and that the methods of one practitioner were not necessarily the same as the next. The idea that there was a coherent "system of witchcraft" that was universally used (even in just one geographical area, like a particular area of England say) is a myth. It looks like Gardner was the first to actually produce anything like a coherent philosophy and religious system that was presented as being "witchcraft" and passed on to others more or less as a system.
So, what does this all mean?
It means that if you want to explore witchcraft, realize that it is your own individual and personal path that is important. You are unlikely to find anyone who will practice exactly the same way you do. Sure, there will be overlap with others but everyone is different and finds different things work for them. Use the symbols that seem to be most relevant to you, regardless if they are old or new. Research the history of things, whether they are symbols, prayers, rituals, ideas, and expand your understanding of those things. Get as solid a grounding as you can in the topics that interest you so that you can truly make up your own mind about them based on real information. Finding out how others use ideas and symbols can uncover information that can help you grow. But be creative, too, and invent your own connections, meanings, and relevance. Many Wiccans and witches (and mystics of many religious persuasions) consider the act of creation to be a form of communion with the Divine; be creative! Look for connections, secret sides to things, patterns in the seemingly random. As you learn to open your senses you'll discover layers of connection and meaning that is all around us if we just look for it.
Read, read, read! Talk with others, listen, but always decide for yourself. What others write or say is always their own opinion on things, and is always subject to bias. There is no such thing as a "one true way" that is correct for all people. The key is to find what is right for you, to follow the path that is yours instead of trying to follow someone else's path.
I'd like to provide a few links to helpful resources on the internet for exploring Wicca and witchcraft, and indeed anything Pagan.
http://www.witchvox.com is probably the best website to start with. They have helpful FAQ files, contact info for individuals and groups around the world, essays on a wide variety of topics written by hundreds of participants, info on various groups (the "traditions" articles) and current news of interest to Pagans.
http://www.religioustolerance.org/ is a good interfaith website that includes lots of info on Wicca and witchcraft. (The guy who runs the site is a personal friend of mine I met years ago when I was in university.)
http://www.selectsmart.com/RELIGION/ is an online quiz that asks relevant questions about religious and spiritual ideas, and then provides a ranked list of religious groups that would likely interest you. It's a good way to find out about religions that might interest you which you might not have known about.
And for some interesting info on the Wiccan Rede, "An it harm none, do what you will" check out the sites
http://www.waningmoon.com/ethics/rede3.shtml and
http://www.draknetfree.com/sheathomas/ As is often the case, things are often a bit more sophisticated (or less straightforward) as is often presented.
Keep an open, yet skeptical, mind about all things!