If you're just starting out in detailing your car, if you think a simple wash makes an improvement, then try claying it to remove the contaminants and then wax it with Meguiars NXT. Then your paint will really pop. NXT is about the easiest to use wax I've experienced with the best shine and ability to hide swirls.
If you really want to get into paint correction then I tell everyone to buy Meguiars D151, it's really good stuff and very beginner friendly. It's pretty much designed for the detailing pros as a one step polish for their customers that just "want it to shine". Best applied by machine. If you don't want to get a really expensive one, a cheapy 6" random orbital will work. I usually just use a wool bonnet on it and it does a fantastic job, better than you'd accomplish by hand.
The protection it offers doesn't last very long but generally next time I wash it then I wax it again. If you want really long lasting protection, more than the NXT can offer, there's not better wax than Collinite, their 476S is inexpensive and lasts months when properly applied.