I cannot tell from your post or your member page where you are, and at least from a cost standpoint, it makes a big difference. If I'm correctly interpreting your member page, then you're somewhere in what is Eastern Time in the U.S., so probably in the U.S. (just statistically, more likely than, say, Quebec, Canada or Santiago, Chile).
In the U.S., the Canon Pro-100 is an excellent printer at a bargain price. The Pro-100 outclasses with iP8720 in almost every way, except that the Pro-100 is slightly larger, and it lacks the iP8720's pigment black ink for printing office-type documents. (I don't know whether the iP8720 uses the pigment black ink on matte photo papers, but its other inks are dyes, so I doubt it would really improve things that much anyway.) No, the Pro-100's prints will not last as well as those from most pigment-ink photo printers, but the Pro-100's inks are absolutely tops among dye-based photo printers for resistance to fading due to light exposure, roughly at the level of some of the worse-performing pigment-ink photo printers (for my detailed but admittedly pieced-together analysis, see
https://www.dpreview.com/forums/post/61374798). In any case, you don't sound like a good candidate for a pigment-ink photo printer (see below).
If the Pro-100 is too large, then the iP8720 is likely to also be too large. If the Pro-100 is too expensive (not plausible in the U.S. but a real issue elsewhere), then look at one of the few current photo-oriented all-in-ones: the Epson XP-8500, the Canon TS9120, or the Canon TS8120. Personally I think the current Canon photo all-in-ones are a significant downgrade from the prior models, and if you can find the recently-discontinued Canon TS9020 for a reasonable price, IMO that is the one to get, but supplies of them seem to be getting scarce.
For the sake of correct information being there for those who look:
a real photo printer, such as Epson 3xxx
If the Epson
R3000 is what was meant, then Epson replaced it four years ago with the P600. Neither it nor its Canon counterpart (the Pro-10) would be good for an infrequent printer because, like pretty much any pigment-ink printer, left unused they're likely to clog and/or use a lot of expensive ink on self-cleanings.
Canon IP8720 seems a good choice. However, although Canon claims the print has 300 years durability. I am very skeptical.
I have never seen Canon make any such claim. I can't imagine they would. If I'm wrong, I'd love a link to the source.
Canon IP8720 uses 6 color inks, 1 pigmented black, 1 dye grey, and 4 dye colors, while Epson WF7210 uses 4 pigmented block 7 colors.
The Canon iP8720 uses 6 inks of 5 different colors: for photo papers, dye inks of cyan, magenta, yellow, black, and gray; and for office-type documents on plain (uncoated) papers, pigment black ink. I suspect that it will print the dye inks other than black on 'plain' / uncoated papers, probably including some matte photo papers, but I suspect the quality will be substantially reduced on some papers.
The Epson WF-7210 uses 4 pigment inks: cyan, magenta, yellow, and black. I don't know where that 7 comes from.
IP8720 is discontinued IP8750 is replacement (at least in UK)
I'm about 93% certain that this in incorrect. AFAIK, the iP8720, iP8750, and iP8760 are all basically the same printer, just the versions for different markets, respectively, U.S. (iP8720), U.K. / E.U. (iP8750), and Australia / New Zealand (iP8760).