Best current estimate of stars in the Milky Way is 110 Billion with an
error rate of +/- 20%.
Most current published estimate of galaxies in the Universe is 125
Billion, as reported in 1999 by the Hubble program. This probably has
a much larger probability of error, probably +/- 50% or more.
As to your other question about types of stars, this is a little more
dicey. The distribution of star types is constantly being skewed as
some star types morph into others, and forther complicated by the fact
that each star class has a different expected life span. The typical
middle-of-the-road star, so to speak, would be about 2-4 time our
sun's mass. Our sun, despite the mythology that it is an "average
star", is actually a rater diminutive star. Eventually, all stars in
our galaxy will become either a brown/black dwarf, a neutron star, or
a black hole. Because all of these objects are very difficult to
account for, especially at great distances, it is unknown how many of
these objects already exist in our galaxy. I believe that visable
stars fall into a bell-curve distribution, with the mean being about 3
solar masses and the standard deviation being (a wild-ass guess) about
1-1.5 solar masses, and heavily skewed towards the left, with a long
flat tail extending to the right for more than 100 stdev's..
Red Giants are very short-lived stars in this form, as they are very
geometricly large for their associated mass. Usually, thet are a
smaller sun in the final throws of death and metamorphisis. This
being the case, their life span is very short relative to other stars,
which can further be argued that since they individually occupy a very
thin slice of galactic time, then they are by definition very rare.
White Super Giants, like Deneb, which are the big-dawgs of the galaxy,
probaly number in the hundereds for the entire Milky Way, or roughly 1
in a billion, while 80%+ of visable stars will fall in the 1-5 solar
mass range. Again, a wild-ass guess based on personal data collection
Hope this helps..