FWIW--The printer is not called "R3800". It's the Pro 3800 (which has been superceded by the Pro 3880)
I have a 3880, that also gets fairly irregular use. I've had to run a few (<10) cleaning cycles, but that's mostly because in the winter my indoor humidity can get in the 20-30% range, which is a little too dry. I should also get a dust cover for it, but I haven't yet.
Everything I've read says that the inks are stable for quite some time. I have some cartridges that have 2/2012 expiration that aren't even installed in the printer yet, and I'm not really sweating it. Epson just doesn't want to guarantee performance of old cartridges or opened ones that have been in uncontrolled environmental conditions. One tip I've read is that if your printer has sat idle for an extended period of time (weeks to months), it's a good idea to "agitate" your cartridges so the pigment particles don't settle. I remove each cartridge and invert it 10 cycles like I was tank-developing film. You don't want to be too rough, as you run the risk of making foam and introducing air into the lines. Best to let the cartridges sit for an hour or so after doing this before you print. You don't want to/need to do this with the R2000 or R3000, since the head movement keeps the cartridges agitated, and (I think) it will purge all the heads when it detects a cartridge swap. I know my old R1900 did this, and the 3800/3880 doesn't do this, as far as I can tell.
Red River Paper has published some pages looking at ink costs of various printers:
http://www.redrivercatalog.com/cost-of-inkjet-printing.html
If you buy the 3800/3880, the printer comes with a utility that shows the actual ink usage of each print job. So knowing that each cartridge is 80ml, you can calculate your ink costs pretty closely. Depending on how light/how dark your prints are, the rule-of-thumb is about 1-1.5ml of total ink per square foot of image area. An 11x14 with 1/4" margins is almost exactly 1 square foot.
Lastly, you might want to look at B&H or Adorama for cartridges. You have to "add to cart" to see the actual pricing, but it runs about $47 a cartridge. Atlex.com/ITSupplies used to have better pricing, but their prices have gone up.
Hope all that helps...
--Greg