ODE, GUI, plotter in Python

[Ala]

Hello everyone.

I am starting on implementing a simulator using python, and since it's
the first time I code in python would appreciate a few pointers:

The simulator will use a coupled ODE for the most part of the
simulation, I plan to use scipy. (Anything considered faster/better
than scipy for solving coupled ODEs? )

I plan for a GUI program with network graph plotting. I am leaning
towards using Qt for the GUI (internet forums seem to recommend it,
anyone got other preferences? )

Since the GUI application will contain few buttons and a plot, I am
planning to implement matplotlib into the GUI. But does anyone know if
matplotlib allows for interaction with the graph plot? (say for a
network simulation, allowing to right click on nodes and disable them
for instance, or alter some other properties of nodes and/or links
across them).

I am just starting out, hence I'd rather get some advice and experiment
a bit for my self as I go along.

Thank you.