Sound quality "podcasting": Mixer + lav XLR mic

Hi - not too sure if this post goes here.
I bad audio quality so I googled. I pretty much know what most of the problems are BUT I would still like to get feedback from the community. 

My wife says she's not spending 200+ euros on equipment when we have audacity that can "solve" everything. I need you guys to back me up.

So...

I plug my USB BOYA lav mic into my MacBook. The sound quality is crap. Just doesn't sound good.

I KNOW about soundproofing so that's not the problem.

Googling - I see that I need an audio mixer or audio recorder + a good mic + decent sound proofing.

My questions:

A need a lav mic for various reasons: Should I get an XLR mic instead of USB mic?

Audio mixer: I don't use instruments - it's for teaching English: Have you got any recommendations? I need great sounding audio.

AUDACITY: For post production. What would I use it for if the mic and the mixer do their job properly?