WARNING: This document is for an older version of iTerm2.
While iTerm2 does not require monospaced fonts, they look much better than proportionately spaced fonts. If you want to use Consolas, you'll need to correct its baseline offset as described at how to fix Consolas baseline.
iTerm2 has the capability of rendering text with thin strokes to improve readability. You can change how this works in the Text panel of the Profiles tab of Preferences.
You can also specify the a "non-ASCII" font in the Text panel of profile preferences. This font will be used for all code points greater than or equal to 128 or for characters with combining marks.