Congrats on the Mustang purchase. I think that if I had to start at zero and wanted to build a challenge car it would be a 5.3 turbo fox. Next to a Camaro/Nova it is the cheapest most well sorted, performance part available platform. That said, does it have an 8.8" rear? If not....get.
I am a big fan of the 460. But...in order to get a trans to work or hold up you will be out of the Challenge due to cost. And if you are out of the Challenge, the 460 is easy to stroke to over 500 inches. If you luck out with a trans and able to use at the Challenge, go NOS. Word of caution, there was a BBF Fox at the Challenge in 2004 or 2006. The owner had to do a lot to set the engine back. His demise was his transmission. IF I built a non Chevy powered Challenge car, a 460 Fox was going to be my poison.
With a SBF, stock ported heads and the right cam makes 360 rwhp easy (BTDT). Nitrous and you're fast. Again, the trans will dictate if it is successful at the Challenge. The Ford trannies, converters and associated cost make them unattractive. I have gotten rid of every Ford performance part except one higher stall C6 converter that would work behind a SBF/Nos combo. BTW, many Ford guys are using T400, T350 or PG transmissions, but its not a cheap adaptation.
IMO, the Chevy engine is the best choice. You mentioned ailing so that issue is not considered into anything I offer. You have to determine if the repair is worth the Challenge cost. We are building another car and the Nova is on hold. The other car is a Turbo LS that we want to build and run 10s for under $1300. We are documenting in case GRM wants to do an article. If not, we (Fuzzy) will post into the build page. The goal will be to show the parts needed to go 10s on a budget. Unfortunately, both projects have been slowed.
Ultimately, (and finally getting to your question) the Chevy offers the best engine/trans options for projects with a Challenge budget. We use T400. Cheap and easily modifiable to get good shift control. I use the early units from late 66 to early 70 do to the internal parts being stronger. Don't touch a 65 or small yoke 66. While they have a 32 spline output they also have a unique yoke and tail stock. The 71 and later need more reprogramming and make the 1-2 shift at 5200 without the reprogramming. But for Challenge money you can get a working T400, drill 2 holes and have a serious transmission. The T350 is viable, but too hit and miss, and definitely needs more work to hold any real power. The SR-71D trans was/is a T400 with a brake that has been together since 1989. We got it through a series of trades and is one of the most common race trannies in the world. The combo of the Chevy engine with the Chevy transmission is why it is hard to beat for challenge money. There are a lot of good engines out there, you just can't go quick/fast without the trans/converter working with it/them. FWIW, the converter is an unknown, but we use it because it only has 4.7% slip which works with the SBC/Nos or turbo....it's tight.
Try to find an early LS1 or LS2 cam. The Sunbird had a 59MM turbo, LS1 cam, dished pistons and ran 10.8. We are expecting good numbers from it on the next series of passes.