Another issue for your 98 will be that the 03 trans will not have a vss provision which your 98 uses. You will have to swap over the tail shaft and housing from your 98 trans to the 03 trans which is not a huge deal.
As far as the shift kit goes, the 97.5-03 transmissions are the same besides the vss provision. 96-97 autos are not as good but you should not have to worry about that. And if its transgo kit... return it and do the jmod. The jmod not only is great as a "shift kit" it has a bonus of extending the life of the trans and will go into gear much faster too, not just shift faster. There is a very detailed how to video on YouTube, I'd just watch that and see what you think.
2000 Mustang GT Steeda build #48. Bolt ons, suspension, Novi 2000.
Just because I give you advice, doesn't mean I know more than you. Its just means I've done more stupid ****.