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}
