Router woes will kill your Netflix
No matter how spectacularly fast the internet coming into your house is, it's really only as good as your wireless router. As you're probably aware, router placement makes a huge difference in connection quality, as obstructions and wacky floor-plan layouts can inevitably create some Wi-Fi dead zones in your house.
Abide by these router rules to keep things running as smoothly as possible: Install it in a central location and keep it off the floor and away from the kitchen or behind TVs/computers (appliances can interfere with the signal). If you continue to have issues, you may want to consider upgrading to one of the many great new high-performance multi-unit systems, which will expand your reliable coverage area (especially in nook-filled homes) and help you better manage the connections by allowing you to prioritize Wi-Fi to certain devices (e.g., whatever device you regularly watch Netflix on).
If you live in a crowded apartment building, you're also likely dealing with interference from the glut of connected devices in the vicinity that are sitting on similar Wi-Fi channels. That's contributing to the drag-on speed of your connection. Modern, dual-band routers offer two frequency speeds -- 2.4GHz and 5GHz -- and generally, running yours on 5GHz will leave you less susceptible to congestion. To manually set it to that band, log in to your router and access the settings page.
If all else fails, the nuclear option would be to go old school and connect your Apple TV/Roku/smart TV directly to the router via an Ethernet cable. Of course, this isn't ideal and is especially tough if your router's nowhere near your TV (though an Ethernet powerline adapter could fix that).