You have to be sure you get a big enough battery. Fords always used bigger batteries than Chevrolets, Plymouth's, and tractors. Those vehicles use a Group 1 which smaller than the Group 2 batteries used in Fords (they come in several varieties depending on the year). A group 1 battery will not fit your battery tray right either, and end up rattling around in the hold down unless you jury-rig something.
Several years after I got my '51 in 1987, it got to the point where the battery needed replacement. All they had locally were generic Group 1 batteries, so not knowing any better, I bought one and installed it. Because of the smaller size, combined with the fact that it was a cheap entry level unit and had probably been sitting around for several years, it never had the Oomph to start the car on hot days. I got in the habit of raising the hood when parking the car for any length of time when driving it in hot weather. That got old real fast. At that time I did a little research and replaced it after a year with a 6 volt Optima in a faux Ford case. This proved to be an excellent solution, and I have run it ever since. Although the Optima's are quite a bit more expensive than "Farm Store" batteries, they are much cheaper in the long run because they last a lot longer. I am in my third Optima since 1997, and they were all running strong when I replaced them. There is just something inside my head that says a 12 year old battery is too old and must be replaced. The first two Optima's are still holding a charge under my bench, for what reason, I don't really know. Also, IIRC, the convertible has a power top, driven by electricity. These take quite a bit of power, albeit for short periods of time that would put further strain on a substandard battery. Long story short; get an Optima.
Also, folks should understand that Optima's are still lead/acid batteries, just constructed differently. Traditional "Flooded" batteries have the lead plates suspended in an acid bath, while an Optima is an AGM (Absorbed Glass Mat) battery. AGM batteries are advanced, sealed lead-acid power sources featuring Absorbent Glass Mat technology, low internal resistance, and spill-proof designs, which give them several advantages over "Flooded" batterie. They are not Gel batteries or any of the newer technologies (LiFePO4, etc.).
Speaking of Lithium batteries, I just put one in my 1967 Corvette. They seem to be the ultimate answer except for the fact that they become ineffective at temperatures below freezing (which is not a problem with the Corvette). They have come way down in price in just the last 6 months. and the newer dual purpose units with the built in BMS (Battery Management System) have a lot more power than lead/acid batteries at 1/3 the weight. Anyone who has owned a Mid-Year Corvette will understand why a lighter battery is desirable in them.