Switching from PDFLaTeX to LuaLaTeX

Question

Code

Consider the following MWE:

\documentclass{article}

\usepackage{inputenc}
\usepackage[T1]{fontenc}
\usepackage{babel}
\usepackage[sc]{mathpazo}
\usepackage{microtype}
\DisableLigatures[f]{encoding = T1}
\usepackage{hyperref} % Used in alot of my documents.

\begin{document}
Test.
\end{document}

Assume I compile using pdflatex (with an up-to-date TeX Live distribution), I then use the setup above.

Questions

I have a few questions:

1. Is \usepackage{inputenc} needed at all when compiling using pdflatex?
2. When kind of packages should I load and how do I setup the font properly if I want to compile using lualatex?

Is the following correct and if not, how do I do it in a correct way?

\documentclass{article}

\usepackage{polyglossia}
\setdefaultlanguage{danish}
\usepackage{fontspec}
\defaultfontfeatures{Ligatures = TeX}
\usepackage{mathpazo}
\setmainfont[
  BoldFont       = texgyrepagella-bold.otf,
  ItalicFont     = texgyrepagella-italic.otf,
  BoldItalicFont = texgyrepagella-bolditalic.otf
]{texgyrepagella-regular.otf}
\usepackage{hyperref} % Used in alot of my documents.

\begin{document}
Test.
\end{document}

Also, is the loading-order of the packages of any importance? (I know that hyperref should almost always be loaded as the last package but apart from that?)

Update

In case I want to remove all ligatures, is the following then the correct way to do it?

\addfontfeature{
  Ligatures = {
    RequiredOff,
    CommonOff,
    ContextualOff,
    RareOff,
    HistoricOff,
    TeXOff
  }
}

instead of

\defaultfontfeatures{Ligatures = TeX}

I found it in Table 11 at the bottom of page 42 of the fontspec manual.

Answer 1

Use the OpenType math font and not package mathpazo:

\documentclass{standalone}

\usepackage{polyglossia}
\setdefaultlanguage{danish}
\usepackage[math-style=TeX]{unicode-math}
\setmainfont[
Extension      = .otf,
UprightFont    = *-regular,
BoldFont       = *-bold,
ItalicFont     = *-italic,
BoldItalicFont = *-bolditalic,
Ligatures      = {CommonOff,TeXOff}%   no ligatures
]{texgyrepagella}

\setmathfont{texgyrepagella-math.otf}
\setmathfont{texgyrepagella-math.otf}[version=bold,RawFeature={embolden=2}]

\usepackage{hyperref} % Used in alot of my documents.

\begin{document}
    Test. -- ---  ff fl fi
    $y=f(x)$ \boldmath $y=\int_1^2f(x)\symup{d}x$
\end{document}

Answer 2

I would suggest the following changes: use fontspec with suitable OpenType font (TeXGyre Pagella mimics Palatino fairly well), and use unicode-math with suitable math font (again, TeXGyre Pagella Math works fine, IMO it looks better than mathpazo, which borrows some glyphs from Computer Modern, and they look different from Palatino). You don't have to drop babel, it works fine. Also, LuaLaTeX have a very nice font search engine, so in most cases it's sufficient to use the human readable font family name in order to find it.

Also, when using one font will become boring, you could find many unicode-math compatible math fonts in this nice question: Which OpenType Math fonts are available?

An example:

\documentclass{article}

\usepackage{babel}
\usepackage{microtype}
\usepackage{fontspec}
\defaultfontfeatures{Ligatures={TeX,NoCommon}}
\setmainfont{TeXGyre Pagella}
\usepackage{unicode-math}
\setmathfont{TeXGyre Pagella Math}

\usepackage{hyperref} % Used in alot of my documents.

\begin{document}
Test. Difficult \emph{test}. Some math --- 
\[
  \int_{-\infty}^\infty e^{-x^2}dx = \sqrt{\pi}.
\]
\end{document}

The result: