Shrimp can be challenging because it overcooks and gets tough/rubbery quickly. You may want to start with something more forgiving, and work up to shrimp once you get to know your grill's heat settings. When you do go for shrimp, watch it closely and pull it off as soon as it's cooked through. Once you master it, it's a great choice because it does cook so quickly, you just have to keep an eye on it.
For things like chicken breast, a meat thermometer is key. You need to pull it off the grill right when it's fully cooked. I have one that stays in meat and has a remote reader so I can monitor the temp continuously from the kitchen, but an instant-read works well too, just go check it periodically.
For any recipe you choose - understand that the times given are approximate at best, and will vary greatly depending on the heat of your grill, thickness of the meat, and more. If you want to nail down a good timeline, slice or pound your chicken into consistent thickness every time you grill.
Dry rub or marinate before you grill; wet sauces like BBQ sauce should be brushed on just for the last few minutes.
One of my favorites is a grilled vegetable combo: I chop an onion, a red bell pepper, a zucchini, and whatever else I have on hand (brussel sprouts, cauliflower, mushrooms, etc) into 1-inch pieces, toss with olive oil salt and pepper, and maybe some Italian seasoning herb mix, toss onto a grill pan, and cook over high heat for about 5-7 minutes, stirring 2-3 times to flip the pieces over. You're going for a light char but still slightly crisp, not cooked soft.
Another carb that works well on the grill is corn on the cob. Pull the husks down, remove the silk, and pull the husks back up. Soak in water for 10-15 minutes, then grill for about 10-15 minutes, turning every few minutes until all sides are browned.