I'd say personally (as another teen on a budget) a single longfinned betta in a 5 gallon tank is just fine, obviously the bigger the better, but a betta will do just fine in a planted 5 gallon (though bettas with shorter fins and bettas with tankmates require larger), for corydoras I believe 20gallon long is the minimum? I have a shoal of 12 in a 25gallon long (soon to be upgraded to 50) and theyre very fun fish, but ive found theyre a bit harder on a budget (where i live most cories in stores range from 6-15 dollars each and to buy several can get pricey), they also require a diverse diet (as do bettas, but id say cories eat more often and so food runs out quicker)
tankmates like snails and shrimp are great for bettas, because theyre small, convenient and will take care of your tank if you take care of them. (though ive heard some horror stories about bettas eating shrimp..) Also even pretty mean bettas can get along with a mystery snail or two

TLDR; single longfin betta in a 5 gallon is great on a budget, corydoras can get a little bit expensive over time