You don't have to become a witch as there's nothing different between a witch and any other human being on the planet just that the witch is a practitioner. I'm not going to debate the existence of weather spells as that's really a topic for another time I believe but as for the existence of magic then it's very much down to your own opinion. Any practitioner is obviously of the opinion that magic exists, myself included, although it's worth adding that magic has limitations but that's something you'll learn whilst studying the basics. As for pretty much the rest of the world they'll tell you that it doesn't, neither side can prove they're right and so until such a time it's very much up to your own opinion and it's not something anyone can really tell you.
As for where you can start out that falls down to 'the basics' I highly recommend checking out the basics threads across the forums, articles and newbie central. Provided you read through them, learn what you can and add your own research you'll be well on your way to understanding and practicing magic. Of course never be afraid to ask when you get stuck or need some clarification but be aware that often people expect you to have attempted it on your own before asking for help.