It's a fascinating topic! While most of the bacteria known to colonize babies comes from the vaginal tract during birth and then later, through breastfeeding, although there is evidence to suggest that microbial colonization may begin before birth.
Regarding what these bacteria are, our microbiomes are composed of probably hundreds of species of bacteria from at least four major phyla: actinobacteria, proteobacteria, firmicutes and bacteroidetes (see the review for more on them).
As for taking antibiotics, I find it highly unlikely that taking antibiotics would completely destroy any native gut flora species. I certainly can't find any evidence to suggest that that might be the case. In general, when we have to take antibiotics, the offending bacteria are a relatively small population, compared to our native species and are less well-adapted to our body environment. Antibiotics work with our own immune defenses to clear our system of pathogenic species. Antibiotics also hurt our native flora, but less so than the ones that make us sick.
As for your last question regarding health, I wouldn't exactly say that having a microbiome promotes better health, so much as that your microbiome is critical for survival and health. There are actually nutrients that we need for survival that we cannot digest without our microbiota and a wide number of diseases, from immune disorders to potentially depression, can arise from an unhealthy microbiome.
As a fun bit of trivia to ponder in parting, our bodies are composed of 90% bacterial cells by count. Sweet dreams... :-)