My first Chinese vases - Blue and white

I found these two Chinese (Japanese?) vases at a local Goodwill shop that obviously had inherited an estate as a donation. There were several other new items (yeah, I'm a regular) that matched the overall theme. The theme was asian special asian items brought back from being abroad. Possibly military overseas and came back to US for retirement with favorite items. There were her dressers, traveling trunks, vases, vase lamps, oriental framed silk paintings etc. Really nice things.
I would like to know more about these befor I give as a gift if any one can help me out. One of them has a signature or initials next to the mark on bottom.
What kind of vase, design, material etc.