Congratulations on your new bike! Way to go. I hope you have many happy rides together!
Picture, please(We love bike pictures!)
As for clothing: You'll definitely want gloves (long fingered if you get cold hands in winter, not if you don't) and a helmet. I wear a beanie under my helmet when it's cold.
I wear the lycra stuff because it's very comfy for the way I ride. You might want to try a pair of lycra shorts, because they avoid having seams in the places where seams aren't comfy. If you're worried about how you look, you might look into mountain biking shorts, which are sometimes looser fitting, or have an overshort. But if you're on a bike, you have to know you're looking great anyway
Biking tights work great to keep you warm, as do leg warmers, knee warmers, and just plain sweats if that works well for you. The important thing for me is to keep the clothing seams from chafing. I wear my biking tights over my biking shorts to take care of the seam issue. (The longer you ride, the more likely this will be an issue; a few miles is usually okay with whatever is comfy, helmet, and gloves.)
This very site (Team Estrogen) has a nice selection of shorts, and great service and advice (you can call and talk to a human!); if you live where there's a good bike shop, you can also go try some things on there.
For chapped lips, make sure you're drinking plenty of water.
You can get little "bags" that fit under the seat or on the handlebars; you can also get a biking jersey with back pockets; they're very handy in all sorts of ways (and comfy!). Some people wear backpacks or little waist bags, if that works well for them.
Welcome to the community and congrats again on your new bike!