A simple solution would be Gnome-Tweak-Tool, also known in the software center as "Advanced Settings". Now you may use this to change the font size affecting the software center, however unfortunately all other applications as well. A recommended way to preform the font change would be to open the settings, change the font size, and then when done with the software center, return it to it's original form, or however you prefer it. If you can't get the application from the software center, due to the small size of the font just paste the following into your terminal -
sudo apt-get update
sudo apt-get install gnome-tweak-tool
Or, click the button below to install for Ubuntu!
Here is what Advanced Settings should appear as, simply click the font size next to the default font to make changes.
Well, you don't really want to mess with the other settings I'm assuming, (Graphics Drivers, or Screen Resolution) But, just to voice other solutions, you could start by seeing if this is the graphics driver, I personally use the open source one because I have no other choice than binary blobs, or the screen resolution could be toned down to make the text appear larger...
Now, as if this wasn't already long enough, Mijyn here wrote a tutorial on resetting the x configuration settings. This could also fix screen flickering. To start, we want to:
Press "Ctrl + Alt + F3"
By doing this, you're opening a virtual console, the appearance may look like DOS, but essentially it's a terminal window, gone full screen with root access. It should ask you to log in, with your password. Now the password will not appear in the window, but don't worry, it's still registering.
sudo rm -f /etc/X11/xorg.conf
sudo rm -f xorg.conf*
sudo service lightdm stop
sudo service gdm stop
sudo service kdm stop
sudo service lxdm stop
sudo service xdm stop
sudo service wdm stop
sudo Xorg -configure
[ -f xorg.conf* ] && sudo mv xorg.conf* /etc/X11/xorg.conf
sudo dpkg-reconfigure $(dpkg -l | awk '{print $2}' | grep "^xserver" | tr '\n' ' ')
sudo update-initramfs -u
Now while this seems like a lot, you can copy and paste this into the virtual console, remember, the paste function when in terminal is "Ctrl + Shift + V" instead of the common "Ctrl + V" used pretty much everywhere else.
You'll now want to restart the computer. You can regain access to the desktop using "Ctrl + Alt + F7". This should reset the X configuration.
If you would like to view MiJyn's work, it is linked here.
Hope some of this can be of help!