Best Linux for a single application & fast boot? (also How-to?) [closed]

"As mentioned by DaveParillo, any distibution can be stripped down to next to nothing. However, building a system from the ground up is probably preferable in your case. This is what Arch Linux was designed for. If you are comfortable with this idea, continue...

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Follow the official or beginner's installation guide to install the base system.

To mount your NTFS partition automatically, open up your /etc/fstab and add the following line (/dev/sdb1 being the NTFS partition and /mnt/device being the mount point):

/dev/sdb1 /mnt/device ntfs defaults 1 0

If you want to be able to log in automatically you will need to take a few extra steps. First, install mingetty from the Arch User Respository (AUR). Here is a small guide to help you do that if you are unfamiliar with Arch Linux.
Next, open up /etc/inittab and change the line that looks like:

c1:2345:respawn:/sbin/agetty -8 38400 tty1 linux

to the following:

c1:2345:respawn:/sbin/mingetty --autologin username tty1 linux

Install X by executing the following commands as root:

pacman -Syu
pacman -S libgl xorg xf86-input-evdev mesa vesa

Configure X with:

Xorg -configure
cp /root/xorg.conf.new /etc/X11/xorg.conf

If xorg is giving you problems you can refer to the wiki.
(If sound is also needed you can follow the steps that are given here)

Edit your ~/.bash_profile so that when you log into TTY1 X will start automatically:

if [[ -z ""$DISPLAY"" ]] && [[ $(tty) = /dev/tty1 ]]; then
exec startx
logout
fi

Edit ~/.xinitrc and include the following (replacing celtx with whatever command starts the program you want to run):

exec celtx
shutdown -h now

Once you quit celtx Arch Linux will shut down.

You also mentioned that you would like a fast boot time. I'm not sure how this compares to what you are looking for, but on a ~7 year old computer I managed to get mine down to 23 seconds by following this guide."