Prior to a fight I will stick to my carries, looking for any strong ult engage opportunities (when the enemy carries group or to catch someone out). Bard's poke is far too low ranged to be used in a 5v5 context. Remember, you're a support. You need to ensure your team can carry out their designated roles in a fight, whether it be to delete the carry, take down the frontline or survive the assassin onslaught. You cannot do that if you die being overzealous.
Positioning in teamfights is very situational. I often have a utility focused build, and will only build an item like banshees 4th, leaving me with 2-2.5k hp for most of the game. As a result, I will take the role of a backline support so as not to get blown up, peeling for whichever carry on my team is strongest (Peeling a 0/4 adc with average cs provides a lower chance of winning a teamfight) or is being singularly focused. This is achieved through strong cc from the Q, Ult, with mobility from E and W.
If the enemy team has a really potent backline, while your team has a couple of backline threats, helping take out the enemy carries may be more ideal. A 1.8s stun on the target is huge, using the mobility from your E to get into position. Hell, even just drawing focus may be enough to help your teammates take the enemy out.
If our team has no backline threats (assassins (Zed, Fizz) / strong dps bruisers (Renekton, Fiora) or flankers (Riven, Lissandra), I will look to ult the enemy carry that is the strongest, revealing pressure from the frontline, rather than using it as a peeling or engaging mechanism. Note the carry may be an extremely fed tank (Mundo, Nasus), that is hard carrying. Taking the most fed player out off the teamfight for 2.5s is invaluable. General rule of thumb is to ult the enemy who is under no pressure. This can also include stopping the utility support from keeping their backline alive (Lulu, Janna come to mind).
In general, I would recommend never ulting members of your team. That tends to set up the enemy, rather than help. If your team just got 4 man flash annie stunned or similar, ult the dps follow up. This buys time and gives the team the option to either disengage or counter engage. There are edge cases, such just before a yasuo ults (note both yauo and bard ult have a one second cast time. You need to ult as the knock up is hitting your team), or just after a delayed ult (zed, vlad, fizz etc.).
Remember, these are just general situations. You need to work out who you will be peeling and who is the threat that you need to deal with.
Tl;dr: Position yourself to support the strongest player on your team. Sometimes it is better to help take out a higher threat. Generally stay towards the outer reaches of the fight, avoiding getting blown up.