I already add the swap partition according the articles you suggest, and configure the mysql base on the tuning-primer script recomendations. Base on this, the mysql database do not crash (before was crashing) but it overloads.
I also optimized the tables via phpadmin. And I think that the tables have indexes because the webpage is base on joomla.
It could be too late now, but if you still have a problem with the database setup, I would advise to use MysqlTunner - this small script will help you tweak config based on your usage.
Also useful, there are some pre-made configs for mysql in /usr/share/doc/mysql-server-5.5/examples. I used the "small" config and it's working quite nicely. I have a fairly low-traffic site running on a 512 meg droplet, and with apache/mysql/php/postfix/proftpd all running I'm looking at around 300 megs free. Also should mention this is using a Debian 7 image.