First, you say "range of 150 miles minimum" for the antenna. You would be talking some serious hardware, and a tall (think permit required) mast, really an unrealistic setup for most.
I currently live right between the Miami and Palm Beach stations, so get a LOT of channels with a very reasonable (up to 50 miles or so) antenna. A Clearstream 2v ( the v means it has a VHF dipole for VHF stations, which are actually quite rare nowadays). I actually have a VHF, you might not need it. You can get them with mount and cable for around $100 (I bought mine on Amazon, since I already have Prime). https://www.antennasdirect.com/store/ClearStream-C2-VHF-Long-Range-Combo-Complete.html Another website http://antennaweb.org/ will tell you what you can receive in your location with reasonable ease. It tells me "Up to 68 channels from 28 over-the-air stations may be received at this location." Last scan I did I know I got 82 or 84 on both a Sony and a Samsung TV (and the Tivo).
Picture quality is better than cable (really, it is!) If you want the "cable" experience, the Tivo is ideal, even if not cheap. Just like a cable DVR, it downloads the program data so you can see what is playing, and integrates everything including search across multiple streaming services. Netflix, Amazon, Hulu, Vudu and now Plex. All except Plex are integrated in the search, so it makes it easy to find things from one interface. My wife has enough problems with just that, but I also have a Roku (which isn't hard to use). Lots of different options with the Tivo, my Premier has 4 tuners and you can also install a cable card if you go back to cable. The spare room I use a Tivo mini, and a Moca network adapter (basically uses your TV coax cable as a network connection). This allows the Mini to stream any recording, or grab a tuner for live viewing.
The Tivo is expensive (I buy mine with lifetime service, but monthly service is available). Lifetime service is about $500 extra, but monthly is only $15. Since I tend to keep mine for a while, the liftetime service pays off after 3 years or so (33 months). I still record shows on an old Tivo Premiere that I expanded with a 4 terabyte hard drive, and can play them back on any of the other two Tivo devices. The program guide and the ability to just create "record every episode of this series" is what you are paying for, and it works very well.
The Roku simply gets more streaming, and at least right now, Tivo doesn't have SlingTV. FYI, Showtime can be added to Hulu, and HBO to SlingTV. Switching inputs however confuses my wife, so she sticks to the Tivo and has no problems finding something to watch. The remote with a keyboard works well for searches.
I know this exact setup also worked well for me in the Phoenix area, just with fewer channels. My wife would have nothing to do with the idea of a PC streaming on the TV, so this works VERY well for my needs.
I forgot to add, I travel a lot, and have the Tivo Mini on a Slingbox M1. http://www.slingbox.com/products/slingboxm1/features.aspx
Really works VERY well. I get between 5.5 and 3 meg streams and can watch anything on my tablet from any place that supports that high data stream. It will work at lower speeds, but at that data rate you really can't tell you aren't watching directly. I use a Kindle but know it works well with almost anything, including my phone. I do have a high internet bill from Comcast/Xfinity, but I use it to work from home a lot too. They just announced in my area a data cap policy, I'll have to see what I use now.
FYI, Teamviewer works really well too, for remote access of your machines. I've been in IT for 30+ years, and I highly recommend it for personal use.
I'm not a big sports fan, but I do know MLB streaming is quite reasonable, looks like $25/year?
It has an app for both Tivo and Roku, but I've never subscribed or used it.