Do some more research. A friend in town bought the 4800 last year and loves it. BUT, it did only come with starter cartridges of about 30ml each to get the printer charged and start using. He then had to buy over $600 of ink in a short time to get up to full production. That is how Epson shipped it. If the same is true for the 4880, then that should be factored into the cost. Can anyone with a 4880 verify?
The 3800 does come with a full set of 9 - 80ml cartridges. That's about $450+ of ink included.
The 4880 as well as the 4800, and 4000 before it all ship with 110 ml cartridges (so does the 7880 and 9880). AFAIK there's never been an epson starter cartridge. Somewhat more than half the cart is left after charging/purging. The matte black is not included but the kit to switch blacks is. For the amount of printing the original poster describes the ink included with the printer will last a very long time, especially the darker colors. I use 1.5ml/foot as a rough guideline when calculating costs.
For the comment about the 3800 being from 2006 I think this is completely irrelevant. The 4880 is virtually identical mechanically to the 4800 and the 4000 and the small changes are incremental. Take the badges off and it's nearly impossible to tell them apart. But I would take this as ---> If it ain't broke don't fix it. The only real changes are the printhead, inkset, and OS software between the 4xxx models.
For the choice between the 3800 and 4880 I think it depends on how you envision using it in the future. Personally I haven't noticed a real-world difference with the VM ink and think it's a red herring to encourage upgrading. The three big differences I see are 1) roll paper, 2) cost of black swaps, and 3) expected lifespan. If the usage will remain relatively low and you have no need for roll media then you might be better off with the 3800 and the relatively inexpensive switches between matte and gloss blacks. If there is a plan or hope to ramp up printing in the near future, particularly for professional printing you might be best served with the 4880. If occasional experimenting and personal printing are the only planned usage then the 3800 might be the more economical choice in the long run.
For the ink switching I'll make a blatant generalization and say that most people seem to go through a stage where they try many different types of papers and then settle on a few that they prefer and will use a single paper for almost all of the finished photo prints. I'll go further out on a limb and say that most people's preference will boil down to gloss or matte and not a lot of both. Different story if you are printing professionally of course, but even then it's a pain in the butt to deal with more than 3 or 4 types of media. As a photographer that does my own printing I use 2 papers and one canvas almost exclusively.
Personally I have a 4880 that replaced a 4000, gloss ink only. I have a 9880 on matte ink only. I've never switched blacks in either printer. The epson printers are extremely well built, a proven design, and can be expected to run for several years printing all day long. The 4000 printed the equivalent of 18,000 8x10's over almost 4 years without a service call. It is big and bulky though and if you intend to switch back and forth between black inks frequently the 3800 could be much cheaper in the long run. Though I use Canon equipment for photography the reliability and support problems with the ipf scared me off. I don't think HP has a model in this league.
Take all of the above for what it's worth, YMMV.
Good luck and happy printing!