The logic between the tall wheels is to get a short stiff sidewall while retaining an overall tire diameter. The reason for that is to improve handling through wheel and sidewall stiffness. My own opinion is that in most cases the 20 and 22 inch wheels are a case of if more is good, too much is just right. The 20's might make sense on a vehicle designed for maximum handling, but ride suffers because of the stiffness.
Have you priced 20 inch wheels and tires? Usually when people say 'on a budget' they mean on the cheap, and 20 inch wheels and tires are not cheap.
I have two old trucks that are currently drivers (three if you count my '91), one of them my total investment, including a set of new wheels and tires, is less than the retail price of 20 inch wheels and tires. A few years ago I took this particular truck on a 3200 mile road trip, pulling another car half that distance.
The other runs 15 inch Cragar mags I found on craigslist and actually represents an investment of about three times what I expect 20 inch wheels and tires would cost today.
My point is that while there are reasons to run the tall wheels, unless you score the right set used for cheap, they could easily be a budget buster. Running 20's on my '72 Chevy would double my investment in it. Running them on my '55 1st GMC would mean spending one-third of what I've already spent to gain no real handling benefit and hurt the ride characteristics.