You need a conversion box to use the older television set. The government was giving them away free during the conversion period, but think you'd have to buy one now. The newer set would be a better bet. I am sure you could plug in the same type of coax cable as the cable company signal uses, but connect it to an antenna instead. In fact, that is what I am using now, and now that the programming is digital, the picture quality is better than the satellite system I was paying for previously. My antenna is on the roof, the same antenna that came with the house but never used since I bought the house about 20 years ago. I live about 50 miles from any station, but if you live in town, I understand there are other types of antennas that can be used, that look like a laptop computer screen, and you point the screen in the direction of the station you are trying to reach. Understand they are highly directional, and think you need to be either close in, in town, or high on a hill, with a good view.
You are right about netflix. I only pay $8 per month. No other fees, although it does not have a lot of the movies I would like to watch. Unlike satellite and cable systems, there is no hook up to a phone, so no way to order additional, costly add ons through a t.v. menue. You could call directly to add on a service where you can order some movies on disk, that they do not provide by streaming, but that is an additional service, and you know what you are doing when you do it. Not a surprise at the end of the month like satellite or cable.
You do not need an antenna advertised as a digital antenna. This is a scam. You want an antenna that pulls in both the VHF bands ( channel 2-13), and UHF bands (14 on up). Some antenna's advertised as digital only give UHF, and do poorly in the upper portion of the VHF band (or not at all). UHF is thought to be more line of sight reception, and in my case, I believe that to be true. My brother is located on the top of a hill in Seattle, and gets reception all the way to Canada, line of sight. I'm located on the flats in the Willamette Valley of Oregon, and barely get Portland stations, 54 miles away, as the bird flies. (but mostly the lower, 5-12 VHF channels, Channel 49 UHF comes on and off through the day, and depending on weather)