See https://www.raspberrypi.org/documentation/installation/installing-images/README.md for installation. The basic boot for Raspbian on the Raspberry Pi 3B is two partitions/filesystems on the system micro SD card, one for boot and the other for root. The boot filesystem is the first vfat (Windows) partition and the root filesystem is on a Linux partition (more details at How does Raspberry Pi boot?). (New options allow booting from other devices, see https://www.raspberrypi.org/documentation/hardware/raspberrypi/bootmodes/ .)
BerryBoot use the boot filesystem as a boot manager and use squashfs for the OS(s). It saves space, but very hard to update.
NOOBS, NOOBS Lite, and PINN (https://github.com/procount/pinn) use the first boot filesystem and a SETTINGS filesystem to select an OS boot filesystem, which boots and load the OS (Raspbian, Retropie, ...). NOOBS has Raspberry Pi support. NOOBS is larger file as it contains Raspbian with option to download other OS(s). NOOBS Lite and PINN are smaller file and requires internet connection to load any/all OS(s). PINN has more OSs to select from and is popular.
To select a different OS with BerryBoot, NOOBS, NOOBS Lite, or PINN just reboot and use the keyboard to select which OS you choose to use. The default is the last selected. (It is possible to change a selection in SETTINGS to predetermine which OS will become the default on reboot (not tried on BerryBoot).)
Another option would be to just download and install Retropie (https://retropie.org.uk/) as it will also install Raspbian Jessie (New Raspbian is Stretch) as Stretch is not currently supported by Retropie. Exit the EmulationStation with F4 and you will be in Raspbian Jessie Lite with a command prompt.
You could also buy a NOOBS card, plug it in, power up, and you are good to go. I would suggest starting with NOOBS or PINN installs on your first try. You can always buy more micro SD cards and try different options to see which you like the best.
The displays is a different question. From web searches it appears that a touch screen and/or a HDMI monitor can be connected to the RPi 3 (https://www.raspberrypi.org/documentation/hardware/display/). I only use HDMI monitor/TV. Plug in the monitor, power on the monitor before powering up the RPi and it self configures the resolution. There are some configurations in the /boot/config.txt file.
