Nobody has asked the important questions:
1. What speed of service have you purchased from your cable company?
2. What speed of service did you have at your old place?
3. What type of connection did you have at your old place? I GUESS it was not cable? Otherwise, why are you purchasing a new cable modem? Maybe you were renting from the carrier?
4. Do you REALLY mean you will only use it for Netflix using your Firestick? So, you won't be using an iPhone, iPad, Android device, Nest thermostat, other iOT devices, etc. etc. etc.
Based on your stated requirement and reading between the lines, you over-paid. Your cost could have been $0, or very close to that.
Cable modem speeds have been increasing, with many companies now offering gigabit service or even more. Consumers need to buy new modems to take advantage of these speeds. You should be able to get something adequate for your needs very cheaply on resale sites, or on "buy nothing" sites, or in a local resale shop.
When I dumped the cable and switched to WebPass (gigabit service delivered to building by radio, now owned by Google Fiber - no modem needed it's an Ethernet jack) I took my cable modem to a recycling center. Since it was working, they probably put it in their store for sale. You could have gone (for example - sure there are local examples) to the University of San Diego Electronics Resale Store and picked it up for I'd guess $10 or less.
If you've purchased a low-end speed tier, you don't need the latest cable modems with a gazillion bonded channels. It won't make it any faster.
As well, you've stated that your Firestick is "right next to the router". N, AC, 2gHz, 5gHz, AX, none of this matters to you. So, ditto, (assuming you've purchased a low-end speed tier) none of these are going to make it any faster.
Netflix recommends 5mbit/sec for HD quality.
ANY WiFi router will provide this speed easily, especially with the Firestick right next to the router.
If you do have an iOS device or Mac or PC on your WiFi, we can suggest some speed test utilities to try. It's also likely you can download some speed test app on your Firestick (sorry I'm unfamiliar with the details of Firestick...)
[automerge]1580072067[/automerge]
the only issue I’m having is that Netflix shows/movies seem to be loading quite a bit more slowly than they were at my old place.
"Loading"? Explain what you mean. Does Firestick download the whole show before it starts showing? Doesn't it stream, like most/all similar devices? Do you have interruptions once it starts playing?
[automerge]1580072305[/automerge]
You’ll find it hard to cross 50 Mbps with your current modem.
50 Mbps is 10X more bandwidth than they need for their stated requirement.