First off, I wouldn't recommend trying to hit directly off the grass for a very green beginner unless they start by teeing the ball up at first just to make contact. I like mats for beginners because they are more forgiving and the last thing a beginning golfer needs is to worry about uneven ground, hitting from a worn out divot infested sun baked ground, unless you find those rare gems of a grass driving range. Once the ball striking gets better, then it's time to move away from the mats and find a nice grass range so you can learn to take divots. Small steps first... you gotta crawl before you walk.
Don't start off trying to take a full, super long backswing at the start. Try a simple 1/2 swing (where your arms are roughly parallel to the ground) to start just to start grooving the feel of the takeaway. Don't worry about where the ball goes, that will come in time. Just focus on making contact with the ball for now. Keep in mind that THE most important fundamental part of golf before you even hit a ball is your setup (aka addressing the ball). That would involve proper foot position, club position(s), your grip on the club, shoulders, spine angle etc.
Hit a bucket of balls at a range and decide if it's something you really think you can get into. If you feel strongly that you'll stick with the sport, I say, buy the best forgiving clubs YOU can afford but ask an instructor or a friend who is technically savy not to be confused with cocky and if they recommend or seem biased towards something, ask why or why not. If they can't give you an answer, see an alternative source for info 'cause they seem to be blowing smoke up your a$$.
Some folks say buy a cheapie $200. set. If you are the type of person that is known to pick up hobbies and drop them in a heartbeat, maybe you should buy the cheapie set. If you're the type that tends to get wrapped up into it and will stick with it for a few years and play an average of 15+ rounds a season, buy the best you can. Confidence in your equipment goes a long way. I've seen regrets over and over from the friends etc. that I've brought into the game.
An very entry level set of clubs would cost you around $300. A mediocre set would be around $800-$1000. A very nice set would round you up around $1500. A damn fine set will cost you over $2000. easily!
As a beginner, if you're of "average" height, then I don't normally recommend getting properly fitted for your clubs other than overall club length. The reason being is that you don't have a fixed swing and proper stance which WILL change in the future as you get better. Some clubs can only be adjusted by length only anyways, more so on the cheaper clubs.
Now, the next step BEFORE you even buy clubs would be to seek professional help by seeing a qualified instructor. A good instructor will advise you on equipment etc. and most have loaner clubs for teaching with.
If you think you're hitting the ball "okay" (doesn't always go straight but you can get the ball in the air once in a while) and I'm not talking Tiger Woods like, I DON'T recommend going to a large course with par 4's and Par 5's! The reason being is that if you've never been on a course, playing a course longer than Par54 can make you hate the game, not to mention, the group behind you will start screaming obscenities at your group. Stick to what's called an Executive Course ie. a course made up entirely of just par 3 holes (par meaning the number of shots it should take to complete the hole from tee to holeing the putt). Good places to cut your teeth and nobody gives a hoot or how long it takes you to play are Dentonia, Cresthaven and Unionville. If you handle those well, then move up to Rolling Hills Classic Course, Bathurst Glen, Mill Run Highland to name a few. Play with some friends who've played somewhat and they can fill you in on golf jargon and course etiquette.
One of the better instructors I've seen teach is a guy name Carl at the Markham Golf Dome (they have an outdoor range too). He charges $55./hr and does a full video analysis of your swing etc. Some instructors know their stuff but can't teach while others are the opposite... this guy knows his stuff from entry level to very advanced.
For the golfers out there, if you want some great golfing info etc. check out
www.golfopinions.com forum. TONs of free info and golfers willing to help other golfers out.
Good luck and welcome to the sport.