SEO Main points?

Alright, I'm new to SEO, but not site development.

From today's studying SEO, I've gathered that SEO is comprised mainly of content, meta tags, and (inward?) linking. Having unique content also would help a great deal. Good html helps(I believe).

That being said, I've just been contracted to help optimize the search capabilities of a website.

This website is a nested table nightmare! Would it benefit the SEO to replace it with a much better(and more accessible) layout using div's, span's and css? (Also proper summaries for the divisions.)

Yes, almost certainly, so long as the page flows in a logical order.
These might be of use:

http://www.alistapart.com/articles/seo/
http://www.alistapart.com/articles/accessibilityseo/

I don't think that the meta tags are important anymore. They are too easily abused. Anyone care to share more info on the subject?

I don't have any meta tags and the bots seem to keep coming back for more.

My site is a nested table nightmare! but I'm working on that.

I think yahoo and msn still care about meta tags

A few minutes on Google confirmed that for Google and MSN, the meta tags are not important. There are varying theories as to how important they are for Yahoo, but it seems agreed that they are important to a degree.

As Yahoo makes up over 30% of my traffic on some sites, it might not be a bad idea to target it. In any case, Meta tags can't hurt, if not done in a spammy fashion. And don't use the same description and keyword meta tags on all your pages.

for some of my pages, yahoo shows meta description in SERPs instead of portion of content