I posted the initial question and thought I would come back to share my experience with the printers after I upgraded to Mavericks in case others are wondering about compatiblity of their printers. (Thank you Guitarman777 for offering to update on your printers. I could not wait! It was a slow day with nothing to do.)
A little background. I have two identical iMacs and only upgraded the secondary computer so far. I have four printers attached to my network, one is wireless (epson), one is on the router (1606dn) and two older ones are attached by USB to the primary computer. (HP 2420 and Canon ip4700.
HP 1606dn - on router - worked immediately
Epson Workforce 545 - printed immediately. I have not tried scanning as I have never had it set to scan on the network
HP 2420

Not so good.
Canon ip4700

Not so good.
Both the 2420 and the ip4700 tried to print, but it kept saying it could not find the printer.
Called Apple support since I have Apple Care and they directed me to HP and Canon saying if the companies had not given Apple drivers for Mavericks, I needed to contact them directly. But the tech kindly gave me his direct line to get back to him if I got the run around. (That is why I love apple tech support!! They follow through)
But before suggesting I call HP, the tech had me remove the HP, which I did, and try to reinstall it. The computer did not see it any more. I tried several times, but the large box that came up only listed the two printers I had already installed and that were working. There was no option for NEARBY PRINTERS as suggested.
While I was on hold with HP while they looked for someone who could help, I was playing around with the printer setup and all of a sudden.. a different smaller box popped up when I clicked the + sign to add a printer and it showed NEARBY PRINTERS. By adding the two non working printers, I am now able to print on both.
But I cannot figure out why the type of pop-up box keeps changing. You'd think that by clicking the + sign, it would bring up a consistent dialog box.
Anyway.. the point of this long winded comment is that all four printers attached to my secondary machine are working under Mavericks. I probably won't be upgrading the primary machine for a few more days. Enough drama for one day! I think the reason I was able to get them to print is that they were installed under Lion. I have a feeling a new install might not work.