I'm okay with a little fading over time.
Inkjet dyes don't do "a little" fading. If you hang them on a wall, they may fade FAST and BADLY. I've seen inkjet prints that spent 1-2 years in a hallway with only indirect daylight and the 'black' had faded to an eggplant purple. Dyes do have the attractiveness of offering a somewhat larger gamut / higher saturation, and they're less prone to causing clogs in the inkjet head. I don't trust dyes for photo prints if they are going to be hung on a wall, or need to have a lifetime of more than a year in dark storage.
Which comes down to: I don't trust inkjet dyes, period. The problem with inkjet and dyes is that there's no real protection against environmental influences; i.e. UV light and free radicals (ozone etc.). This is different from the dyes in chemical/RA4 color paper, which are suspended in a gelatin emulsion that locks them off from environmental factors and involves a top layer with a very effective UV filter, not to mention radical scavengers and other forms of protection against aging.
Maybe I'm just getting more and more conservative as I learn more, IDK. I stick with pigment for inkjet inks.
Back to your original question: there's so much subjective about the question as well as the answers that it's impossible to give a solid answer.
I'll revert to the "forum default of answering", which is basically telling what I did and then leaving it up to you to make sense of it. I'll preface it with "anything with decent quality will cost decent money". It's certainly true for inkjet printing in my experience.
So what I did when I didn't want to spend a ton but I did want to make decent inkjet prints, was keep an eye on second websites and jump on the first pigment Epson that seemed attractive to me - which at that point happened to be a 3880. This was some 8 years ago or so. The first one I had a look at in real life had a head alignment issue, so I passed on that one. The second one was a private seller and the unit was in good shape, print quality seemed OK. The unit cost me €350, which was a good deal back then. I think these printers still go for about the same price, despite being long in the tooth by now.
Initially I just went through the inks that came with it (a bunch of half-full cartridges and the typical one or two spares for black). When the time came to purchase new ink, I bit the bullet and got a set of refillable cartridges and some 3rd party ink from InkjetMall. The initial investment was (back then) around €500 if memory serves, for the cartridges plus a batch of ink. I bought new ink a couple of times since that, but still use the cartridges since they can be refilled and reset.
Throw in some money for paper and let's say I spent €1000 in the first year or so. Print quality is good enough for me, for photos. I know I could get better, but I'd have to replace the printer, inks, everything and I'm not willing to go there.
The advantage of the printer I have is that it at least offers a couple of channels per color; it has a high- and a low density magenta and cyan, a single yellow and three densities of black, with a distinction between photo black and matte black. The different densities per color make sense; to date, I've not seen a single halfway decent color print from a printer that only uses a single channel per color. It's OK-ish, but not really 'photo quality' in my book. There are usually visible banding problems with those systems, too. On a decent paper, my old 3880 prints fine without visible banding and the inkjet dots are only visible with a magnifier; they're not obtrusively present.
I could have saved me some money if I had opted for a smaller printer. Mine prints up to A2+ and I think A3-sized printers are more easily available and cheaper as well. In terms of ink, it doesn't matter much. Ink is relatively expensive.
If you want to save money, see if you can get a second hand printer in good nick and a type that allows you to use 3rd party inks. If you stick with OEM inks, you'll spend a ton on a per-print basis. I have serious doubts about the OEM inks being demonstrably better (different gamut, more lightfast) than the
good 3rd party inks like those of InkjetMall and probably (hopefully) InkOwl. Paper makes a difference too, quality- and cost wise. You can get reasonably cheap inkjet paper that produces reasonably OK prints. Really nice paper is costly; think Hahnemuhle Baryta. I think it's worth it for the few Really Nice Photos you want to print; the bulk I print on generic, mid-range paper that doesn't cost an arm and a leg. Don't expect anything except absolute crap (there's no other word for it) at the bottom end of the market price-wise, both for ink and paper.
I did shop around for a new/second hand printer some months ago when my 3880 was acting up. I was appalled at the poor availability of affordable 2nd hand printers, especially decent ones, and the relatively high prices. I ended up repairing my geriatric 3880 and continue to use it today. It's an old beater, and despite its occasional hiccups and constipations, it has served me surprisingly well given the abuse I've thrown at it.
Hope this helps in any way.
In hindsight, I think I lucked out in that I got decent/fairly good quality at a reasonable price. I wish the same to you.
PS: inkjet printing for photo books involves the challenge of making a presentable book from individually printed sheets. I have little experience in this department and insofar as I have any, it's not particularly encouraging.
PPS: lab-printed RA4 prints on decent paper (DPII, Maxima) are really quite good and probably still the best bang for your buck.
