How to simulate and or calculate complex impedance of LC circuit
Smith invented his chart to do this stuff before computers were powerful or ubiquitous enough to run simulators.

Whereas a simulator will show you what a circuit will do at a given frequency with given load and source impedances, it won't help you imagine what a circuit will do if you change the load slightly. More importantly it won't help you guess what type of component you should add to bring the response to where you want it. A simulator certainly will not offer to add components for you.

The thought process when gazing at a Smith Chart will often be 'my locus is here and it needs to be there, so I need a sniff of series C'.

Ideally, you'll learn the graphical approach on a Smith Chart, confirm it on a simulator, and check a few points with a calculator for a fully rounded understanding.

That will put you head and shoulders above what most students do today which is whack everything into a simulator and hope.

However, knowing how to use a simulator is way better than not.

I'd probably start with putting a simpler circuit into a simulator, that had a Smith Chart display for the results, understanding what it showed you, then building the complexity up to what you have drawn. 

You could do worse than to search for the original Smith publications where he describes how to use his chart. Very readable.