Do the Trinity first, it's much easier than modding the Corona. My first Corona needed a post fix adapter and to bridge the missing resistors near the NAND header. It was much more work. Trinity is way less work. I would get the JR programmer because it can program Sonus 360 if you want to later on.
I would also like to suggest getting some magnifying glasses? The soldering points are tiny and these things make it so much easier.
I also bought a fiberglass pen to remove the thin coating on the soldering points. I don't know if you know how to take apart a slim, but the Xtools kit makes it much easier and I would also recommend getting an Xclamp removal tool. If you are doing the Trinity, hands down the Ace V3 with SRGH is the best. The V3 works great on the Corona too.
Some Coronas have a 16mb NAND that don't need an SD tool and then there's the 4GB NANDs that do. So you could potentially need an SD tool, a Postfix adapter and the Ace V3.I got my postfixs and SD Tool from PhenomMod. Weekendmodder has a video on how to tell if you need a postfix. It helped me a lot. I don't always agree with the things he says or his methods but he does have a lot of experience.
I have a list of the stuff I recommend. You can decide what you do and don't need.
Ace V3 Glitch chip: https://www.amazon.com/gp/product/B07SCZP2L8/
JR Programmer V2: https://www.amazon.com/gp/product/B01MTUWLVJ
Optional (makes your life easier or recommended for longevity)
Slim Xtools Opening Toolkit: https://www.amazon.com/gp/product/B07DNX4ZPZ/
Magnifying glasses: https://www.amazon.com/gp/product/B0827WBQYQ/
X-clamp removal tool: https://www.amazon.com/gp/product/B07BV42DSM/
Artic Silver Thermal paste: https://www.amazon.com/Arctic-Silver-AS5-3-5G-Thermal-Paste/dp/B0087X728K/
Header Pins (for flashing Ace V3, just easier, not required): https://www.amazon.com/gp/product/B07PKKY8BX
Fiberglass Pen: https://www.amazon.com/SE-7616SB-Fiberglass-Scratch-Brush/dp/B003NHDITW/
3 pin male pin header
https://www.amazon.com/MCIGICM-Header-2-45mm-Arduino-Connector/dp/B07PKKY8BX