David has listed quite a few possibilities. Here I want to highlight two that I find particularly interesting.
Gentium
Gentium is an award winning font that supports a wide array of Latin scripts as well as Greek an Cyrillic. You can use it with:
\usepackage{gentium}

Note that I had to use "c" instead of "s" to get the correct final sigma (thanks to @Thérèse for spotting this).
GFS Didot
GFS Didot is a free and faithful digital version of Didot's Greek, a.k.a. "apla". GFS has paired the Greek glyphs with Palatino like Latin glyphs, which I do not particularly like. I like the combination with Palatino, though:
\usepackage[sc]{mathpazo}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{udidot}
\linespread{1.05}

The sc option can be replaced with osf to get old-style/lining figures. Some might claim that Pagella is the better choice for Palatino, but I have preferences.
Times
In the comments you mention, that you are using newtxtext, i.e. Times, as text font and that you like GFS Didot. Unfortunately, GFS Didot is to dark compared to Times, but you can try other fonts, e.g.
\usepackage{newtxtext}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{txr}
Here the Times plus GFS Didot combination, that I do not recommend, with full example code:
\documentclass[a4paper,12pt]{article}
\usepackage[greek.ancient,italian]{babel}
\usepackage[T1]{fontenc}
\usepackage{newtxtext}
\usepackage{substitutefont}
\substitutefont{LGR}{\rmdefault}{udidot}
\begin{document}
Dal greco\begin{otherlanguage*}{greek}
br\'aqistos
\end{otherlanguage*}(brachistos), e\begin{otherlanguage*}{greek}
qr\'onos
\end{otherlanguage*}(chronos), tempo.
\end{document}
