As JosephWright explained, you can perfectly well use both inputenc and fontenc:
\documentclass[11pt]{article}
\usepackage[T1]{fontenc}% generally best to load this before loading the font
\usepackage{tgpagella}% alternative to MinionPro
\usepackage[utf8]{inputenc}
\begin{document}
The pound sign one way : \pounds, or another \textsterling
\end{document}
inputenc sets the input encoding i.e. how the characters you type are encoded. fontenc sets the output encoding which tells TeX where in the font particular glyphs should be.
The reason you get a dollar sign when you do not load fontenc with the T1 encoding is that you are then using the default encoding, OT1 and there appears to be at least one bug, but probably two, in the font configuration for tgpagella (and probably the other TeX-Gyre fonts since they all share the same encoding files).
OT1 only has 128 slots whereas T1 has 256. This means that there is not room for both the dollar and pound sign. Originally, TeX could not deal with encodings containing more than 128 characters. The way TeX originally coped with this limitation was to put the dollar sign in the upright font and the pound sign in the italic. So if OT1 is active (e.g. because you don't load fontenc with another encoding), your code will produce dollar signs instead of pound signs because the dollar occupies that slot in the upright font. To avoid this, LaTeX uses the following code:
\DeclareTextCommand{\textsterling}{OT1}{\hmode@bgroup
\ifdim \fontdimen\@ne\font >\z@
\itshape
\else
\fontshape{ui}\selectfont
\fi
\char`\$\egroup}
and further defines \pounds in terms of either \mathsterling or \textsterling depending on whether you are in maths mode or not.
So \pounds and \textsterling should behave as expected. However, it does not. For some reason, TeX tries to load the ui shape for tgpagella. Since this doesn't exist, it substitutes the upright shape which, of course, gives you the dollar sign. This suggests that the relevant font dimension has not be set correctly as the code should cause it to try \itshape rather than attempting to load the non-existent ui shape. However, even if you force \itshape, you do not get a sterling sign but, rather, an italic dollar. So the configuration has apparently put an italic dollar in the italic font for the OT1 encoding rather than the upright sterling sign.
Avoiding such complexities is one reason T1 is recommended. Others include the fact that many accented characters are included in T1 whereas if you use OT1, TeX has to create them from the unaccented glyph plus an accent. This is less satisfactory in terms of both the visual appearance (in many cases) and copy-and-paste. Again, this is because of limitations imposed by the 128 slot limit.
inputencandfontenc: both are useful, but for separate tasks. – Joseph Wright Mar 13 '14 at 17:59