Are you male or female? Different crotches require different advice.
Females require jeans that are loose enough in the crotch that the big fat “blue jean” welted seam doesn’t embed itself in your…jeepers, there’s no polite synonym for “extremely tender place where all the important things all fold up together”.
If you spend an hour or two riding with a big blue-jean-type welted seam tucked up snugly in your…crotch…you won’t be able to pee for several hours afterwards, as it causes a certain kind of…bruising…down there. Here speaketh one who has Been There.
And if you are wearing rather tight jeans, when you get up in the saddle, try to pick out your seat, unobtrusively. Yes, I know it’s tacky, but we’re talking “extreme discomfort” if you don’t. 
Can’t speak for the guys, I expect one of them will be along in a minute to talk about…boy crotches… 
Moving along…The next big question is:
Are you riding Western or English? Big cowboy saddle, with the “horn”, or itty-bitty postage stamp saddle? It makes a difference in what kind of stirrup to expect, which makes a difference in what kind of shoes you can get away with. Listen to Ruffian, she speaketh truth, and I would add that a big wooden Western stirrup is more forgiving of less-than-desirable shoes than a skinny slippery metal English stirrup (if you don’t feel like going out and buying some boots just for one ride). The important thing for both styles of riding is that the shoe have a distinct heel of some kind, like oxfords. And with shoelaces, not slip-ons.
What’s the weather like there? Hot sunny days require a hat of some kind, and a long-sleeved shirt (preferably light-colored). Yes, you can burn on your arms even if you think you’re tan. A straw cowboy hat will do, but make sure it’s got a chin tie strap, or it’ll blow off the minute you lurch into anything faster than a walk. There’s a reason Clint Eastwood has that black dingle-dangle thing hanging down there, it’s not just for looks.
The riding helmet is an excellent idea, but if you’re riding Western, you’ll look like an effete English dork if you show up at Cowboy Bob’s Horse Rental wearing one. 
And yeah, I suppose you can wear a baseball cap, if you must…
But even a Wal-Mart straw cowboy hat is muchcooler, in both senses of the word.
Are you going to be riding on a trail, or going around and around in a riding arena of some kind? It makes a difference–what’s everybody else wearing? You can get away with workboots and a baseball cap at one of those “pay by the hour” Western trail-riding establishments, but if you walk into the Holy Equitation Riding Emporium for your 30-minute riding lesson wearing workboots and a baseball cap, and you’re surrounded by a dozen or so teenage Olympic riding team wannabes, all tricked out in their shiny boots and cute lil black riding helmets–well… 