The conventional wisdom here is go with the diesel because simply puts diesels were built with towing in mind.
Well your right 1st gen Dodges with the cummins in them are overpriced. You can get them around here for about 2500 bucks. With about 300k on them. Most of them autos. IF you can find a cummins with a 5 speed within your budget then go for it.
I would buy the gas truck. You are on a high school budget. While a big block is not really cheap to fix, it is cheaper than a cummins. Alot of times you can find good running big blocks for less than a grand. I have been looking at cummins engines for a year now, I can't touch a running cummins for less than 2k, they are dang near worth more out of the truck than with the whole truck.
A big block will tow just fine. It may tow a bit slower and it will get worse mileage but at least here diesel is so much more than gas you have to double the mileage to break even.
That said I back in the day when first gen cummins were brand new I got the chance to tow with one vs a big block truck. On hills the cummins would walk away from the big block, but on flatter ground that big block would hang right with the cummins.
Consider a mid 90s Ford with a 5 speed, they are great trucks. The fuel injected trucks will get 10 mpg towing a car, sometimes more if you are gentle and you can push them hard. The 5 speed will give you almost enough gear selection to hang pretty good on steep grades.
So while the conventional wisdom says diesel is the only way to go. Gas trucks can tow and big block trucks can tow pretty dang good