For my project life, and other journaling, I have been using this printer Canon SELPHY CP900 Color Photo Printer.
For my project life journal, I found if I printed instagrams "bordered" - it prints them as 4x4 inch squares. My page protectors have 3x3 slots, so I just trimmed them down to fit. I did not seem to loose anything much from the photo doing that.
This spread shows perfectly how I cut them down to 3x3 with no problems:
If I choose to print "unbordered" it prints a full 4x6 version. I don't have any examples of this to share. I seem to always crop my photos down to squares even if I don't post them on instagram.
For this spread in my daily album (below), I resized the photos in photoshop and saved the files to an SD card and printed them directly from the printer (it has a SD card slot). Note that I wanted these small, so I made one 4x6 image in photoshop with them all on it and printed it that way.
The one thing that I was mislead about was wireless printing from my phone. I use an iPhone and had to install an app to do so over a wireless connection (it was a free app). It works pretty good, sometimes I have to close and reopen the app to get it to work.
I mostly print iPhone photos - but you can use the SD card slot to print photos from your camera as well.
All and all it is a great little printer. You do need to purchae the paper and ink together, I like The 108 print set that I get on Amazon.