Some good advice here ... using an outfitter that has rental guns is a good idea. Take the Beretta auto-loader ... easiest on the shoulder for high volume shooting.
Check references carefully ... and contact a few to verify. Packages start at around $ 1500 USD, but most are in the $2500 USD range and up. There is a lot of info on Google ...
try Argentina + dove hunts. The better operations are those that constantly advertise in the higher-end sporting magazines like Shooting Sportsman, Sporting Classics, Gray's Sporting Journal, etc. An "Orvis Endorsed" or "Beretta Trident" is a good indicator as to lodge/outfitter quality and reputation.
Many of the outfitters offer a 3 day and 5 day package, some with x-amount of shells included ( eg, either 1000, 1500 or 2000 ) in the package price. Permits ( $150 ) and tips for bird boys ( $40 ) and the lodge staff ( $40 ) per day are suggested and not included. The meals (lots of beef) & wines (Malbecs) are superb. Find out how long the average ride from the lodge to the dove fields are. Shells 12 & 20 ga., beyond any included in the package price are currently $ 12 USD a box. Expect your shells to be Spanish or Italian in origin.
Some lodges are like hotels in high season ... many groups of hunters with 6-10 in each group. A smaller operation is perhaps preferable. Enquire about capacity.
This is a "high volume" shoot ... hardly a "hunt". If you can stand an average day of 500 shells, then go for it. Some shoot much more (remember that $12/box !) if the flights are good ... maybe upwards of 2500 or more shells per day. One lodge as I recall reported a US client buzzing through some 9000+ shells in one day, accounting for in excess of 6000 doves ( I can only ask ... "Why ? " ) Although the birds are classified as " crop destroying pests" and the birds are not wasted, a couple of flats a day for 3 days should be enough to satisfy .... but of course you will be encouraged to shoot more.
The primary dove species is the Eared Dove zenaida auriculata very similar to the mourning dove of North America, but a separate subspecies nonetheless. Two varieties of pigeon are also common to the Cordoba area ... the Spot-winged Pigeon patagioenas maculosa and the Picazura patagioenas picazura ... so no Mourning Doves
or White-winged Doves which are more common to to Canada, the US, Mexico & the Caribbean.
Do your homework carefully as to which lodge/outfitter will suit best suit your budget & expectations. Certainly worth doing once and for those that can get their head around the numbers, many do book return trips. If you are going that far, you may want to do a 5 day or longer "combo-package" that also includes ducks, geese & perdiz.... all species which are pretty much unique to South America.
