To form, is it one of the oldest?
Yes, it appears it is.
Good link, Vast. And that should not be surprising. Large spiral galaxies like ours appear to be quite mature.
Also note that today's MW galaxy is likely a very different critter than the one which formed soon after the Dark Ages ended. For starters, most of the stars which make us look like a spiral are very young; for seconds, we've been snacking on small fry galaxies from Day One, and we're still eating!
Are "Milky-way" type of galaxies common?
According to Spiral Galaxies - Spirals are not the most common type of galaxy.
Our neighboring Galaxy, M31 or Andromeda, is also a spiral galaxy. Both are in the Local Cluster.
Milky Way Galaxy Wikipedia
Milky Way Spiral Structure
The Milky Way Galaxy - A Grand Design U. of Oregon
also on Wikipedia -
List of Galaxies
Groups or clusters of Galaxies
Just wanted to note for clarity that, even though they're not the most common type of galaxy, spirals are not unusual. (i.e., not a rare type)
Separate names with a comma.