Sauron was a better, safer and smarter choice compared to Ungoliant and Glaurung.
Melkor was both fearful of and unable to control Ungoliant. She had her own will and desires. She was both a threat and formidable foe for him. In fact had it not been for the aid of a number of Balrogs, who managed to drive her away, it's possible she may have devoured him. Anyway her hunger got the better of her and she devoured herself (how one manages to eat one's own mouth is beyond me, but I digress).
Glaurung whilst a devastating foe against the Elves, was much lesser than that of Gothmog or Ungoliant, not a Maia or something from the Unlight, merely an experiment of Melkor's. Once he sacked Nargothrond and had collected all the treasures of Felagund he spent much time simply guarding his hoard; thus this being of more importance than being helpful or serving Melkor.
Gothmog may have been the only real good choice as a Chief Lieutenant instead of Sauron. As Lord of the Balrogs, he had many impressive victories under his fiery belt. He was the only real equal to Sauron, appearing first as Captain and later as General of the armies of Angband. In fact had he not been destroyed by Ecthelion he may have proved to be the better choice as Sauron was ultimately quite disloyal and cowardly (this would have been unknown to Melkor at the time).
Melkor would have found Sauron's cunning and ability to convey information through spying very useful. Sauron, like Gothmog had a terrible, powerful physical presence, but Sauron also had powerful magical abilities as a sorceror. I think this would have tipped the job in Sauron's favour. Plus for a variety of reasons he was the only one against those that you mentioned that actually survived long enough to be of continued worth.