Jiujitsu is a brutal sport, it's often called human chess. Joe Rogan, Russel Brand, and Wiz Khalifa to name some - are just a few people you may heard of who roll. Rolling is sparring in Jiujitsu. When you're at an experienced gym it's going to be full of all belt ranks. Don't let that discourage you from training at new gyms though, because lots of one on one with a blackbelt instructor for standard rough $100 a month is still a killer deal. When you're at an experienced gym though, there's belts of all ranks and the lower rank belts are going to be less graceful in their grappling and more likely to injure you.
The blue belts (first rank above white) all have something to prove against the new white belts. Your purple and brown belts will be a little more forgiving but also submit you more quickly. The black belts will take time to teach you stuff while you're rolling. So with that being said, you have a serious scramble fest against other white belts and newer blue belts. They're all going to kick your ass, rub your ears in the matt, and make you sore regardless. Even the other new guy who you best most times, will tap you out. It's a humbling experience really.
Your job as a white belt is simply to survive. Try to retain what you learned in the drilling and technique repetition between rolls. While rolling, don't fight armbars to the death. Save that for competition. I was the white belt who would risk losing an arm to get out of an armbar, DON'T BE THAT WHITE BELT. Don't be afraid to tap. Be afraid of injury. Just focus on surviving. In practice you'll slowly learn how to gauge what levels of submissions are dangerous and what range of motions you can still prevent or escape from them. When you first start Jiujitsu, everyone is going to kick your ass. Unless you have serious wrestling and grappling experience, just get ready to have your ass kicked.
After awhile, the ass kickings will be less bad. You'll pickup on the body motions that create the space and separation you need to breathe. You'll learn to trap arms and legs, pass guards without using your elbows as ice picks, avoid going for the full mount and find comfort with side control. It's a process, but you'll learn it. Just focus on surviving and keeping your body intact. Nobody is going to judge you for tapping. Instructors will pull you to the side and tell you, that you're going to seriously injure yourself if you take practice too seriously. The people who stay in Jiujitsu are generally fairly humble, forgiving, and helpful.
So just survive, learn, and try to have fun with your Jiujitsu family! Breath, take your time, ask all the questions, and pat your rolling partner on the back when they tap you out. Because they just taught you how to avoid it the next time!