For the sake of closing this question, here is a summary of the comments:
inputenc are incompatible with
fontspec lets you use any TrueType and OpenType font easily (with commands like
\setmainsfont that just need the name of the font you want to use), but require you to compile your document with a modern TeX engine such as
lualatex. These two engines in return forces you to use
utf8 encoding, and are therefore incompatible with
\inputenc. Also, as
fontspec is a kinda upgrade to
fontenc, you shouldn't load
For more information on
pdflatex, read these questions:
If for some reason you want or need to compile with the legacy
pdflatex, you will need to find a font that is available in Type1 format, and load it "the old way".
The best option seem to be TeX Gyre Termes, loaded by the
tgtermes package. Part of the modern TeX Gyre collection of fonts, an initiative aimed at providing high quality versions of standard fonts for TeX and in OpenType format, it is a replacement for the older URW Nimbus Roman font, that can be loaded by the
mathptmx package (AFAIK,
nimbus with math support added, but I might be wrong).
Another option is the New TX font, loaded by the
newtxmath packages (you need to load both).
Note that for both these options you should also switch to Cork font encoding, i.e.
For more about Times replacement, you can read What is going on with all these Times clones?