There is no one best Analytics dimensions to analyze conversions: a tailored analysis is part of a tailored business strategy and can be done with a combination of existing Analytics dimensions and /or with the creation of new custom dimensions.

Custom Dimensions boost your Analytics analysis: they allow you to get more from your website based on your business goals, site structure, web marketing strategy, conversion action…

Author Custom Dimension

For example: if you run an inbound strategy with a blog and your blog is written by different authors you may like to know which author leads to more conversions. You can extrapolate this data with a custom dimension (assigning an author to his pages in your blog).

Product View

Another example? If you run an ecommerce you can track a Product View (with SKU) (products your visitors view during their visit). Some might not get purchased, but could lead to other conversions. This could also help you build Predictive Marketing strategies.