It looks like you're interested in using Garalde-type text fonts. If so, the free-of-charge Cardo and EB Garamond font packages should be of interest to you. The Cardo font is, AFAICT, not distributed with TeXLive; it may be downloaded from the font creator's own website. EB Garamond is distributed automatically with TeXlive (and with MikTeX too, I believe).
Other font packages you may want to consider -- even though they're not true Garaldes -- are CMU Serif, GFS Artemisia, GFS Bodoni, GFS Didot, Junicode, Linux Libertine O, and Old Standard. (I'm drawing heavily on this posting and especially egreg's answer for the preceding list.) Depending on your operating system, further suitable system fonts may be available. E.g., if you use MacOSX and MacTeX, you could consider using Garamond Premier Pro, Arno Pro, and Minion Pro. Naturally, there's also a huge number of commercial fonts that might satisfy your font-related needs.
By the way, if one uses XeLaTex or LuaLaTeX along with the fontspec package, one should not load the inputenc package. XeLaTeX and LuaLaTeX can handle only one input font encoding anyway: utf8.
The following example was compiled under LuaLaTeX. To increase comparability, the fonts are scaled to have the same "x-heights" (via the fontspec option Scale=MatchLowercase). Some fonts are more "compressed" than others; there's also considerable variation in terms of "color", i.e., "darkness". The Greek characters of Junicode may be too slanted for some tastes.

\documentclass{book}
\usepackage{fontspec}
\defaultfontfeatures{Scale=MatchLowercase} % scale fonts to have same x-heights
\usepackage[greek.polutoniko,english]{babel}
\setlength\parindent{0pt} % just for this example
\newcommand\teststring{book title Περί τὴν ἄλωσιν τῆς Kωνσταντινουπόλες}
\newcommand\test[1]{%
\medskip\setmainfont{#1}#1\par\teststring}
\begin{document}
\obeylines % just for this example
\test{Arno Pro Regular 10pt}
\test{Cardo}
\test{CMU Serif}
\test{EB Garamond}
\test{Garamond Premier Pro}
\test{GFS Artemisia}
\test{GFS Bodoni}
\test{GFS Didot}
\test{Junicode}
\test{Linux Libertine O}
\test{Minion Pro Medium}
\test{Old Standard}
\end{document}
betababelpackage lets you input these letters with diacritics from a regular Latin-lettered keyboard. For an example, see https://tex.stackexchange.com/questions/389105/typeset-greek-words/389110#389110 – Michael Palmer Oct 09 '17 at 23:46fontspecpackage, you shouldn't be loading theinputencpackage as well. – Mico Oct 10 '17 at 00:00test_greek.auxand recompile the LaTeX following egreg's instruction. Your first attempt will have put some rubbish in the .aux file which will keep generating fatal errors. – alephzero Oct 10 '17 at 00:05betababelpackage to meet the OP's typesetting needs (which include use of thefontspecpackage and utf8-encoded input). – Mico Oct 10 '17 at 13:19