Commercial labs is a good suggestion. While I am forced to use WHCC as only one offered by my website (excellent product - bu minimum $12 "your cost" order and surcharge for drop ship), there are excellent competitors in MPix/Millers, Bay Photo, etc. While drop ship to customer is nice, may prefer to you then you custom ship with your 'special touch thank you', flier suggesting other products, etc.
Commercial lab printers are not only the large machine, but a different technology. They use Kodak (or Fuji) E-lux?? paper that is color negative using chemicals to process. It is not until you get into the Fine Arts offerings that you get paper designed for ink drop - dye based or pigment which is the basis for all personal/commercial printers from set paper size to wide rolls.
Prices at commercial labs are very competitive and many photographers - wedding/group event in particular with their large runs and multi person orders - make a solid living using them. Also an excellent choice as a business startup as minimize startup costs and can see if a viable business.
The Epson Eco-tank appears to be a good alternative. I never looked at them as my concern was idle time with lack of use and ink dry up. First thing that stood out pigment ink. The only question is if they will handle cardstock weight paper. Epson didn't specify in the specs however, in the accessories it offered post card size/weight paper, individually cut that may be too small. Many models offered below your stated budget, but don't know what the differences are as they all - even entry level - come with scan, copy, fax features you probably won't use.
Then there are large format printers 13" to 48" wide paper. With these you will need a paper cutter - except 24" and higher printers, roll paper only, do have a horizontal cutter. Looking at set sheet size, such as 17x22, if able to print a 3 x 4 grid, that is 12 per sheet, then cut. Pay attention to print speed as may be too slow (Canon in particular @4 minutes vs around 1.5 minutes for Epson). The 24" roll printer leaves them in the dust.