One of the best things about golf shoes is that (at least some of them) they are waterproof. I tend to play a lot in the early morning, or in/after a rain, or I step in a puddle, etc. So I always get ones with 2-year waterproof guarantees. But if that doesn’t matter to you - or certainly just starting out - any court shoes would be fine.
Finding balls isn’t theiving. I can’t remember the last time I bought a ball. Its all in knowing where to look. But most new balls are pretty good. Mainly, you’ll want to choose between one with spin and one for distance. And as a beginner, it won’t make that much difference. Top-Flites or Pinnacles will do you fine for a couple years.
Of course some times an idiot will hit someone else’s ball. No matter how good or bad you are, it is a good idea to mark your ball with a sharpie. Just a dot or line somewhere - so you will always be able to definitely tell if a ball is yours.
Clubs, well, there are all kinds of choices out there. One really neat recent thing is the hybrid club. Often called a rescue club, or an iron wood. Basically takes the place of a long (1-4) iron. Much easier to hit. Any beginner and most accomplished players should carry at least 1.
The least important club for you will be a driver. For many people, driver is a very difficult club to hit. You’d be fine for a year or so teeing off with a 3-wood, a hybrid, or even a 5-iron.
I’m also a fan of Ping putters, and mine cost around $100. The main thing is to learn the difference between face-weighted putters like mallets, and toe- weighted blades. And which is better for you depends on whether you stroke straight back and through, or in an arc like a swinging door. Whatever you do, don’t get one of those belly or chest putters!
If you can rent clubs for a while, by all means do that. Your first goal should be to find one club - any club - that you can hit pretty straight pretty predictably. Maybe a 5 or 7 iron. IMO, most beginners would be fine starting with no more than 5 or so clubs. Maybe a putter, a wedge, 7 and 5 irons, and a 3 wood. So it is kinda silly to spend a lot of money on a nice set before you even know how to swing them. You don’t even know what might feel or look good to you.
OTOH, if you buy a cheap starter set and find you like the game, you are going to want to sell them immediately.
Clubs are not 1-size fits all. Have your pro “fit” you. And if you don’t trust him, go into a Golf superstore over lunch some day, or early in the morning when they are not crowded. What is best for you depends on how hard you swing, how long your arms are compared to your body, how straight you stand, etc. Get 2 or 3 opinions before spending a couple hundred dollars on clubs.
You can buy a lot of clubs used, and buy various parts of the set individually. For example, you could start off with a set of irons - say 5 through pitching wedge. Add a putter that feels good, and maybe a used wood, driver, or hybrid. Then, as you get better, you can buy a couple of fairway woods and/or hybrids, and a nice wedge or 2. You can start with a cheap $10, or buy something decent for $50 or so. As far as putters go, it is all about what feels and looks best to you.
Then when you are comfortable, you might want to spend a bit buying LAST YEAR’S new driver (the most recent clubs are always outrageously pricey!) Heck, if you want to try a big driver, get a knock-off for $30 at K-Mart, and if you like it, ask for the real thing for your birthday or something.
Clubs also fall into 2 main categories, for forged blades for pros and those for the rest of us. What you want is the club that is the most forgiving and easiest to hit. Your pro should be a lot of help for you.
Try to find a place to practice, and practice a lot before you hack up a course. Hopefully you can find a practice green to work on chipping and putting. And many stores/ranges have demo days and loaner clubs you can try.
I’m buying a 3-wood this spring, and have it narrowed down to a Titleist, Taylor-Made, Ping, or Tour Edge. My local club has demo days, where I will be able to go to the range and try them out, and simply buy the one I like best. IMO, the only way to go. Of course, I already know how to swing a club, and what I like and don’t like in clubs.
Somewhat counter-intuitively, often times the pro shops at courses will have prices as good if not better than the big boxes. So you might want to shop around (if you want to save mommy and saddy a few bucks.)
Final point, I have long been a BIG fan of Tour Edge clubs. I do not think they make a bad product, and all but their top of the line are very reasonably priced. Unbeatable guarantee and service as well. Just my $.02.
Dress - be comfortable. Women have more leeway than men. If you want to wear slacks, that’s fine. Basically think what you would wear to a casual picnic, where you might be playing horseshoes or volleyball. Something that allows free movement, and doesn’t make you sweat overmuch.
But since you are an attractive young woman - and there aren’t enough of your species on golf courses - o/b/o male golfers worldwide I beseech you PLEASE SHOW US A LITTLE LEG! 
And the MOST IMPORTANT THINGS - keep pace and HAVE FUN!
- I almost forgot, if you have not done so already, you must rent/buy and memorize Caddyshack. “Noonan!”