I'm going to completely disagree with everyone you've heard from and then tell you to listen to me as I've also owned several 65-66 Mustangs (still have a '65 289 hardtop with a T5 conversion), and several 88-89 5.0s, and now own a 96 Cobra road race car and a 98 Cobra daily driver....
Here's why.
Yes, the 96 Cobras ran hot on occasion while sitting in traffic in hot climates. There was a TSB from Ford telling them to make a few changes including an upgraded radiator and a few other parts. Put in an aftermarket radiator (if it hasn't already been done) and you're fine. Chances are any over heating issues that happened have been resolved in the last 18 years by previous owners!
All of the 4.6 DOHC modular motor cars were great cars. Some had minor issues but nothing more than you'd see with any other car. They got better with each revision (like most cars).
Here's the only advice you need to hear: Get the best car you can afford.
Figure out how much you want to spend or can afford to spend and start there. I recently bought my 98 Cobra for $4K. It has a lot of issues but I was prepared to fix them my self. These issues are maintenance things from previous owner abuse. I could have spent $9K and bought a perfectly clean 98 Cobra with no issues but I didn't want to spend that much. I have a race car habit (hobby) to fund!
Anyway, research what's on the market (autotrader.com, ebay, cars.com, forum classifieds) and see what colors you like, what bodystyle (coupe, vert), and things like that. If you MUST have an automatic transmission, then you buy a Mach1.
Each year newer car is a little better than the previous. Again, get the newest, lowest mileage car you can afford.
Have a favorite color? That will help. Ford changed up the color choices regularly. Bright Atlantic blue? Only offered in '98. Competition Orange (one of my favs) was only offered a few years (03-04). If you like black like me? You can go with any year, I own four black Mustangs and a black F350. Also, if you want to spend a little more and get better confidence that the previous owner knew their stuff and took care of the car, start of the forums like here and svtperformance.com. Those cars tend to bring a premium but are owned by enthusiasts. Typically you'll find cars with more performance modifications on the forums compared to autotrader or cars.com.
Any car can have issues but don't let that scare you away. You've done the right thing by asking here first (and hopefully joining the club). Tony runs the best "show" in the country as far as car clubs go and you will never regret the friendships you gain and the camaraderie from a club like this.
Hope this helps! More questions??? Ask away!