A veil is a wedding tradition but it’s up to you if you want to wear one. Some religious services may require one so ask your officiant.
I personally love veils. It’s so bridal and when in your life will you ever wear one again.
There are a variety of veil styles and lengths so if a long chapel or cathedral-length veil is too long for you, opt for a shorter one that is fingertip, elbow-length or even a birdcage that just covers your eyes. A veil has two parts: there’s the longer tulle that covers the back of your dress and the blusher which covers your face.
As for styles, veils are made from tulle but can be trimmed with ribbon or adorned with crystals. Your bridal salon will probably sell a number of options for you to try on with your wedding dress.
You can remove your veil right after your ceremony but practice doing so before your wedding day so you don’t create a hair emergency.
But as I always say, you don’t have to do anything you don’t want to do. It's your day.