To address the "most important" issue, everyone will have a different answer. In some ways it's apples to oranges, just like "what's more important, wearing your seat belt or or exercising regularly?" Both can be lifesaving but hard to compared the "relative goodness". This also depends hugely on your age and life situations (childed or childless, with elderly parents or not, teen or older parent, etc). Those with older kids won't care as much about a vax that saves many newborn lives; those with only infants will not likely care as much about sexually transmitted infection prevention.
My individual point of view is that lifesaving vaccines are most important, modified by one's chance of getting that disease and the chance of cure. As another example: a vaccine for HIV if developed would be #1, because although prevalence (in the US) is low, death rate (for now) is 100%. Hep A vaccine prevents a fairly common disease but almost no deaths and few hospitalizations, so I would rank that at bottom. None of the vaccines in the routine US schedule are considered (by me) to be experimental or dangerous, so I will be avoiding any discussions regarding relative safety.
So against my better judgement, here goes:
HiB (can be fatal or disabling and used to be a frequent cause of meningitis, blood infection, deafness and seizure disorder prior to vax)
Strep pneumoniae (aka PCV13 or Prevnar; similar to above)
MMR (because measles is wildly contagious and can be fatal; in some states we are approaching dangerously low levels of herd immunity)
DTaP/Tdap (in the US mostly for pertussis prevention, because pertussis can kill newborns)
Influenza (very contagious, 30,000 deaths per year in US, vaccine moderately effective)
Hep B (once acquired, no cure and can lead to liver cancer and/or cirrhosis)
Polio - still around and very disabling
Varicella (very common, very contagious, hospitalization rate ~1%, death rate ~1/10,000 in the US)
HPV - VERY common, can lead to cervical (and anal and throat) cancer
Menigococcal (MCV) - less common but very serious and sometimes fatal
Rotavirus (prevents a very common but rarely fatal (in the US) disease
Hep A (fairly common but rarely fatal or disabling)
How's that for a start?
I'm just wondering how I'm still alive. Nine of those vaccines mentioned were never on the schedule when I was a child.