Question about using default router and modem

Tl;Dr: screw ISP modems. If cash is tight, go with a 3rd party router you can slap ddwrt/openwrt. If you've got some money and time, go with something a little more robust.

Modems aren't really a big deal, all they really are is an interface to the cable system's RF signaling, as well as subscription enforcement (speeds, if you paid your bill, etc). Any thing leaving your router is going to be seen by the ISP either there or at the headend, so it doesn't really matter. They make 3rd party modems, but performance increases may be minimal.

Routers on the other hand, I wouldn't trust their gear as far as I could throw it. Perhaps I have a tinfoil hat on, but I wouldn't put it past them to log all traffic before it hits my VPN and phone home, let alone hold and handle my configuration correctly (looking directly at you, Spectrum). I recently got Frontier fiber and they provided an Eero router, and I don't care for that thing (primarily because they're owned by Amazon, and I don't trust Amazon even more than my ISP). For my networks, I pass all traffic through a VPN on the router level so that all my ISP sees is a big blob of encrypted blah (with the exception of streaming apps, whom are isolated on their own network with very strict firewall rules and are not allowed anywhere near my trusted network, only because some get cranky when used over a VPN and they're data vacuums). Additionally, ISP-provided routers have a tendency to lack configuration options, even port-forwarding (useful for gaming, servers, etc). Not entirely sure where your networking skills are at, but I'm guessing you might have some basic familiarity given that you're here and asking.

Most 3rd party routers will give you better performance and configuration options than your ISPs nonsense, and maybe a better degree of privacy (though maybe not). If privacy is your concern, all your traffic needs to be encrypted out of your router through a trustworthy VPN, and steps on your local network need to be taken to ensure that traffic is handled appropriately. Do your research on the brand and company of any gear you're looking to buy, and make sure they line up with what you're looking for.

I haven't messed with dd-wrt/openwrt in probably 10+ years, but they were a great option for consumer-grade hardware back in the day, and I'd hope they still are. The software simply did it's job of routing packets and that was it, no shenanigans. There is a bit of technical knowhow involved, but their guides were great and very thorough. As long as you understand basic networking concepts, it should be reasonably straightforward to set up a basic network.

If you have the money and time to learn, I'm personally a fan of Ubiquiti (when I'm paying for it) and Ruckus (when a client/someone else is paying for it). These are much more involved networking hardware companies and there is a good sized learning curve (and cost), but if you want something to play with and a streamlined network, they're awesome. Ubiquiti has a pretty decent wizard to get a basic network going, and from there you can mess with it at your leisure. Their Dream Machine (UDM) is a great all-in-one router/wifi AP, but it's also almost $300, depending on your money situation.