DMOZ is important but takes a long time. The best way to get into Google is to get linked from an existing indexed page. Automated submissions are against Googles TOS (terms of service) and will not work and the Google submission page will not get you anywhere - links are the only way to get into Google and more links is the only way to climb the SERPs.
This stands for most search engines although a few have paid submissions and directories (Yahoo for instance).
DMOZ is of course a link, but as noted it can take a long time to get into DMOZ at the moment. It is an excellent resource and worth the wait though and I do recommend submitting your site. Ensure you read their guidlines thouroughly though.