It is funny, I fished out of a 12 foot jon for 5 years. It was my first boat, we even fished 3 people in that boat often. However I was 18 years old and so were my girlfriend/now wife and my best buddy. We fished out of it on a very calm drinking reservoir and only with an electric trolling motor. I never felt scared about us in it at all. Now, I would never do that at my age (over 50) nor would I recommend anyone else using that small of a boat for full size adults. Not unless it was 2 adults to fish a tiny pond. Consider most 12 footers have a width of 32 to 36 inches at the rear. Most 14 footers are 36 to 48 inches wide at the rear. That additional width directly equals stability.. Now on a V boat they usually are wider than a jon boat in the back and have the deeper V up front. They automatically have better stability built into a smaller package. With the purpose of fishing with your dad, I would suggest selecting a boat that he will feel more comfy and secure in. A 14 foot jon will be a good compromise and we should be able to find one close to your budget. It sure helps that dad has a trolling motor as you may find a nicer boat & trailer with no motor in your budget. I think several of the boats you showed me look good. My personal choice would be this one https://racine.craigslist.org/boa/5726923911.html. It is the one pictured below. I know that is a little above what you want to spend, but from a complete and ready to go package and safety/ stability standpoint i think I would put that in my yard immediately. The seats are going to be comfy allowing dad to stretch his legs without being on high pedestals. Many of the boats I looked at had installed tall pedestals which are fine on big bass boats or 18 foot wide jon, but they make it "feel" unstable due to the higher center of gravity. If you decide to fish electric only waters you simply remove the gas engine that day and add your dad's trolling motor on the rear as well as a second battery.
My last reservoir rig was a 15 foot aluminum Mod V bass boat. I pulled my gas engine off and added 4 more batteries and two transom mount trolling motors. That boat was terrific to fish out of on big drinking reservoirs here in MD.. I will post a couple of pics so you can get some ideas. Notice I have added some rod holders which allowed us to troll for big white perch. I also added some marker buoys to use when I found fish schooled up on deep structure or shallower humps surrounded by deeper water. I lie the Anchor Mate anchor winch mounted up front nest to the trolling motor Lastly I have a mount sticking up ( the black arm on the right ) for a depth/fish finder. We fished for bass, crappie, perch, cats, walleye,and other panfish on this boat. In this picture you can also just see the black boxes that contained two deep cycle batteries. There were two more behind in the stern area and one more under the front seat in the metal box. With a few add ons the 14 foot V boat above would function the same. It will have a nice V up front to cut the water and a wider flat bottom in the rear. Thus providing a stable platform.
By the way I later removed that 25 hp Merc, off the black bass boat, and sold the Polar Kraft with it reinstalled as it originally was. I then purchased a used 75 hp Merc and installed it on the Lowe bass boat. I did this because we moved to the Chesapeake Bay about 2 years after these pics were taken and would no longer be able to keep two boats or fish those lakes. Here is a pic of the Lowe bass boat as it is now.
Good Luck and let me know how it goes