Leotards offer the flexibility and comfort you need when practicing dance or gymnastics or even just when working out at home. The lack of extra material and the form-fitting nature of the garment reduce the risk of getting your fingers caught in the material (which can break them) and also make your movements more streamlined. One consideration is sleeve length. Some activities require a certain sleeve length for leotards used as part of a team uniform. But for personal or classroom/studio use, sleeve length brings up a number of questions.
Season and Overheating
Leotards come in four main styles: long sleeve, 3/4 sleeve, short sleeve, and strap or tank style. As you can guess, the sleeve length can affect how warm you feel. If you tend to overheat easily, you may want a short or tank version; you can buy warmup jackets and coverups to wear when you are about to warm up in cold weather. At the same time, a lot of practice rooms can have air conditioning running at full blast, and long sleeves would protect your arms from what can be a constantly dry breeze.
In a well-lit room, your arms should be visible when you hold them against your torso. But when you wear a long or 3/4 sleeve leotard in a room full of people, your instructor may not be able to get a good sense of how you're holding your arms in just a glance. The sleeve color, of course, visually blends in with the rest of the leotard, making details harder to discern. It's essential that your instructor be able to see all of your arms to determine if you're holding it properly; improper position in ballet or gymnastics can result in a sloppy look at best and an injury at worst.
How It Looks
This is a highly personal preference, but for many people, a long- or partial-sleeved leotard looks sleeker and possibly more elegant than short sleeves. A short sleeve looks very informal (think of how a long and short sleeve on an office shirt look). Strap-style leotards often make their way into ballet performances as part of costumes, but that's the key — those are costumes that have a specific reason for wanting exposed shoulders.
Those longer sleeves can also cover up minor scratches and scrapes; seeing an adhesive bandage on someone's arm can ruin an elegant effect, even in a practice session.
If you're taking a class and need the leotard for that, ask your instructor about requirements. Otherwise, consider the impression you want to give during practice, and be very certain about what your comfort level is. With those in mind, choosing a sleeve length will be simple.