Do I need to buy new tires when I buy new rims?

[Ali]

Hi. I have a 1998 Honda Accord and was told my rims are corroded and leak air constantly. I am sick of filling my tires with air all the time and want to buy new rims. I would buy aftermarket rims since they are cheaper, but they will still be 15" ones. Do I need to buy new tires or will my current tires fit the new rims? Also, I'm looking at discounttiredirect. Does anyone have any recommendations on good places online to buy rims that are affordable? Thanks