There are tons of options to choose from when it comes to halters. They come in all kinds of sizes, materials, colors, and styles. At the end of the day, it all comes down to two basic designs: regular halters and breakaway halters.
I think that regular halters are great for use around the barn for things like cross-tying or holding for the vet and farrier, but I tend to use breakaway halters for pretty much anything else. I prefer them for pasture turnout because if the horse gets hung up on something the halter will break, which means less chance of injury to the horse and less potential damage to property. If you plan on leaving your horse in a stall for an extended period of time, it is better to use a breakaway halter for the same reasons. Unless you have a horse that is incredibly difficult to halter for some reason, it is usually better not to have a halter on them at all while they're in a stall. Time spent in a stall should be as comfortable as possible for the horse, and leaving a halter on for too long can cause things like hair loss where the halter makes contact with the horse.
I do like using regular halters for lunging; for my personal horse, I tend to use a rope halter when I lunge him because he is very sensitive to pressure on his face and the rope halter makes it so I don't have to do much to get him to stop or turn around. I like using regular nylon halters when I lunge with tack on because they fit well over bridles.
Most people with horses own more than one type of halter, and it's always good to have a backup in case one breaks. The nice thing about breakaway halters is that you can usually buy a replacement piece, whereas with regular halters you would have to replace the whole thing. Everyone has their own preferences when it comes to halters but safety is a big consideration for me when choosing one, and I almost always go with breakaway halters.