Lisa, I think Jason makes a good point. Even though the printer costs a lot up front, in the long term it is the inks and papers that add up. Therefore if you want to stay with Epson, I'd consider moving up to the 3800 simply because of the extra inks you get with the initial purchase, as well as the cheaper $/mL ink for the 80 mL cartridges, as well as not having to change them as often. As added bonuses, you can keep both matte and photo black cartridges in at the same time, even if you need photo black for your glossy prints most of the time, and you have the option of printing up to 17" wide for the occasional big print.
To answer your specific question, though, both inksets for the 1800 and 2400 are supposed to pretty archival, so longevity should not weigh into the decision here. The main difference I would say is matte. I know you don't print on matte often, but the 1800's inks don't work nearly as well with matte papers as the 2400/3800's K3 inks. For neutral B&W prints I would also stay with the 2400/3800 K3 inks and the Advanced B&W driver.