I'm running ubuntu 13.04 64bit on my desktop, I installed Apache2, MySQL and PHP etc.

I wanted to have my web root in /home/afflicto/public_html instead of /var/www. So I went along with this guide:
http://www.maketecheasier.com/install-and-configure-apache-in-ubuntu/2011/03/09
(I did everything from "configuring different sites") as I like the solution more.

Here's what I did:
Installed Apache2, MySQL etc..
copied /etc/apache2/sites-avaliable/default to /etc/apache2/sites-available/afflicto. Then edited it, it now looks like the following:

/etc/apache2/sites-available/afflicto

<VirtualHost *:80>
ServerAdmin webmaster@localhost
DocumentRoot /home/afflicto/public_html
<Directory />
Options FollowSymLinks
AllowOverride None
</Directory>
<Directory /home/afflicto/public_html/>
Options Indexes FollowSymLinks MultiViews
AllowOverride All
Order allow,deny
allow from all
</Directory>
ScriptAlias /cgi-bin/ /usr/lib/cgi-bin/
<Directory “/usr/lib/cgi-bin”>
AllowOverride None
Options +ExecCGI -MultiViews +SymLinksIfOwnerMatch
Order allow,deny
Allow from all
</Directory>
ErrorLog ${APACHE_LOG_DIR}/error.log
Possible values include: debug, info, notice, warn, error, crit,
alert, emerg.
LogLevel warn
CustomLog ${APACHE_LOG_DIR}/access.log combined
</VirtualHost>

I did sudo a2dissite default && sudo a2ensite afflicto && sudo service apache2 restart

I created a index.php and index.html in /home/afflicto/public_html/test/
when accessing localhost/test or localhost/test/index.html etc, I get 403 forbidden error.

What am I doing wrong?

update 1
I have set the owner of the public_html directory to www-data.
Also sudo chmod -R +x public_html && sudo chmod -R 777 public_html
Still same 403 error.

Here's the output of the apache error log:

[Sun Jul 14 06:10:32 2013] [error] [client 127.0.0.1] (13)Permission denied: access to / denied
[Sun Jul 14 06:10:32 2013] [error] [client 127.0.0.1] (13)Permission denied: access to /favicon.ico denied

I was faced with this issue. But I didn't like the idea of changing the group of my home directory to www-data. This problem can simply be solved by modifying the configuration file for the virtualHost. Simply configure the Directory tag to include these

<Directory "your directory here">
   Order allow,deny
   Allow from all
   Require all granted
</Directory>

The Require all granted is a new feature I guess; having a default value of denied.

see this page for further info: http://httpd.apache.org/docs/current/mod/core.html#directory