The only way to get the broadcast networks for "free" by themselves is to get an over-the-air antenna. I've read various posts that suggest you cannot get good signal from all locations in The Villages but this is your only option. You'll get HD quality TV with a good antenna mounted in your attic and properly positioned to receive the signal from the towers. You're going to need an amplified long-range antenna - probably costing you ~$100 not including installation.
Best Over-The-Air Antennas in 2019 | CordCutters
The Golf Channel is owned by NBC Sports. The only way you are going to get this channel is to purchase a device such as the Roku stick and subscribe to NBC Golf or some other service that includes this service. As another post suggested, if you find a way to get this channel "for free" you've probably found a backdoor somehow.
If you get the Roku stick there are a number of apps that aggregate free channels in one place with a nice interface. The best of these I've found on Roku is Pluto TV (
Pluto TV). You don't need a fancy Roku stick. I'd probably go with the Roku Premiere or Streaming Stick. Both are under $50 when not on sale. Depending on how your HDMI port is situated on your TV you may need a short HDMI extension as the Roku plugs directly into the HDMI port and for some TV's mounted to the wall this could interfere with the mount or the wall. Check your HDMI port and if you don't have 3-4" of access from the port to any obstruction you'll want to get a short extension cable.
One more point on the Roku, Fire Stick and other such devices. In all cases these products are simply portals that allow apps to run that actually link the TV to the internet. There is no device that I'm aware of on the market that behaves like you've asked for, other than a cable set-top box. You're going to have to scroll through the apps, select the app (such as Pluto TV or the Golf Channel app) that provides the channels you want and then you'll use the interface that they've designed to select the show/channel that you want to watch.
FWIW: It really doesn't matter but your 100mbs internet is not 100mbs at each wireless connection/device regardless of how "strong" the signal is. The actual speed for each device connected to your router/access point is going to depend on a lot of factors, many of which are outside your control and likely beyond the technical capability of most consumers.