Pages with mulitiple, non-linear elements

I’m looking for suggestions, after a lot of fruitless searching. I’d like to build static pages with text blocks rather than linear text, so “Heading 1” plus text at the top left, beside “Heading 2”, at the top right, in a second column. Then “Heading 3” plus text below “Heading 1” and a little further down “Heading 4” plus text below “Heading 2”, etc. Does that make sense? I’m basically looking to have a little more control over the layout of an individual post.

I’d also like to display, under one of my headings, recent posts from the appropriate category, plus a few words from the start of those posts.

Any ideas? What plugins should I use?