I track my Ford powered 260Z. My personal experience is that transmission gearing is extremely important to getting the most fun on the track.
In Florida, you will most likely be doing track days at Daytona and Sebring. Both tracks have very fast sections.
Before doing track days, I autocrossed the car. In autocross, you only really need second gear if you have the right differential / tire height. I used Hoosier 275/35-15 tires and have a 3.36 rear end. With a 1.94 second gear in a T-5 and 6,500 rpm, 2nd gear was good for 73 mph.
When I started doing track days, I needed all the gears. I had replaced the stock 1st through 4th with G-Force gears and shafts, but fifth gear was still stock. With that set-up, these were my gear ratios.
1st 2.95:1
2nd 1.94:1
3rd 1.33:1
4th 1:1
5th 0.59:1
Worked great until I needed 5th gear. that big a drop absolutely killed the fun (no acceleration in 5th). After my first time a Daytona, I changed 5th gear to 0.81:1. The .81 gear absolutely transformed the car. Now 5th gear is warp drive.
The transmission that you show probably doesn't have a good selection of gear ratios, and probably won't hold much power.
If it were me, I would get the new TKX with the close ratio rears. That transmission will handle the power and maximize you fun on track. If I didn't already have so much invested in my T5, I would get a TKX.
This is the TKX I would get:
https://www.speedwaymotors.com/TREMEC-TCET18084-TKX-Close-Ratio-5-Speed-Ford-Manual-Transmission,452007.html?srsltid=AfmBOoq-x1paVSDoNvgI38myLy79UBWXzZFW-QeQ4bK1_vWnSHM7bEEJ
Gear Ratios
1st - 2.87, 2nd - 1.89, 3rd - 1.28, 4th - 1.00, 5th - 0.81