Having done the research and analysis, here are the most important SEO factors, from the highest priority to the lowest.
The Web site's Link Popularity -- The number of outside links, assuming all links are medium to high quality, counting new sites, and ignoring spam.
Anchor Text of Inbound Links - Targeted keywords.
Keywords in the Title Tag - Shows in search results, easiest to optimize.
Domain Authority/Back links of the Linking Page - The number of quality inbound links that point to a page from which your link comes matters. The more authoritative that page, the better your link is.
Topical Relevance of a Linking Page - A link from an authority site on the topic is worth GOLD. Links from topically relevant but less authoritative sites are also valuable, considering that's where Google is going; this will be more valuable in the future.
Age of Site - The older your site, the better. Buy an old domain if you can afford it
Internal Link Power Distribution - Make sure to heavily link pages you want to rank internally, consider anchor text.
Total Amount of Outbound Links on a Linking Page - The more links are on the linking page, the less rank value is passed with your link.
Link Distribution of the Site in Communities - the more your site is cited in online communities, the more important it is in the eyes of search engines.
Keyword Within Content - The importance of this should be obvious.
External Link to Other Pages/Site - Link only to quality sources.
Age of Link - Links are like wine; they get better with age.
Age of Linking Page - This, too, is like wine.
Linking site ranking for your keywords - If a site ranks for your keywords, then getting a link from that site is very valuable.
Text Surrounding the Link - The more relevant the text, the better.
Internal Link Popularity of Linking Page - This works the same way as inbound links. The more good ones, the better.
Domain Name Keyword Use - This helps with anchor text distribution.
Amount of Indexable Content - More content is good, but don't pin all your hopes on content volume. Without links, it doesn't go far.
Rate of New Inbound Links- Too many coming in too fast can set off red flags without evidence to justify a spike (events, search volume, etc)
Keyword Use in H1 Tag - Plug keywords there.
This is my shot at classifying SEO ranking importance. Do not use it as an absolute list; consider it more as a guide. Do more research and read articles to learn more.
Search Optimization 
