Should I buy WiFi with Spectrum or buy my own?

Buy your own.  Get an Asus WiFi 6 router.

Buy your own modem as well.  Get one on their approved list (they manage it so it needs to be on that list).  Get one that has 32 channels down by 8 up. More channels, the more stable your speed in my opinion.

IF you buy one of those $40 pieces of trash, you will be unhappy.  You get what you pay for and if you don't pay, you will be unhappy.

What I am telling you to buy has a break even time of maybe 3 years. 

My nephew works for spectrum as in installer, gets his equipment free.  He bought a RT-AX88U rather than use stuff Spectrum has.  That one appears to be sold out in many places.

I suggest you get specs from Spectrum so you are comparing the right router to theirs.

a decent Netgear is better than anything most ISPs will give you.

you might also consider a wifi extender if you have a large home, to cover greater area.

If you buy a router you get...a router. Internet service doesn't magically appear.

if you're going to stay with Spectrum for longer than 7 months, I'd buy the router.   That's obviously when it's paid for itself