It’s 1720. A ship carrying large amount of silver and other desirable goods, sinks off the coast of Peru. I possess the rough knowledge of where it went down and a generous budget, as well as manpower. What are my options if I want to retrieve as much of the cargo as possible?

Well, to start with it depends substantially on where (how far) off Peru your hypothetical ship sank -- the Nazca Plate pushes up against the west coast of South America there, and the Atacama Trench reaches a maximum depth of just over 26,000 feet in the Richards Deep. It's tough to go that deep and recover objects in 2016; in 1720 it would be utterly impossible below 100 feet or so.

But, let's say for the sake of the argument that your hypothetical ship sinks in harbor, or not far off the coast, before the fairly narrow continental shelf falls off into the depths. Your options in 1720 may be several, depending on the state of the wreck: did it sink by heeling over and mostly in one piece, or did it beat itself to death on a rock or a sandbar, or did it burn or explode? Is the hull mostly intact, mostly shattered, did it drag for a long time over the ground or did it break up on a reef or rocky coast?

In any case, you're not going to attempt salvage unless the hull is reachable by divers, which before SCUBA diving would limit the depth to not more than 100 feet, or a simple diving bell that could reach a bit deeper and allow people to work longer.

If you just want to get goods off the ship, a diving bell would probably be your go-to. After Vasa sank in 1628, Albrecht von Treileben got a contact to retrieve guns from the ship; he was able to raise most of its armament in the two years 1663-1665. The process would have been to send down a diver(s) with a line to attach to the cannon and raise it from the surface; most loads like that would have to not only be cleared from the hull, but also attached to the surface with enough area for it to run through. Similarly, in 1687, Sir William Phipps salvaged jewels, gold and from a sunken ship off Santo Domingo using a diving bell, though he was mostly salvaging chests and other loose cargo.

Assuming the hull was in mostly good shape and the ship sank by sudden flooding, you could also try to salvage the entire hull using an old method of salvage whereby you attach strong cables to the hull, run the cables to hulks or pontoons (filled with water), make them taut with capstans, and then pump water out of the hulls to raise the load. You would then move the ship shoreward until it grounds, and then repeat the process tide by tide until the ship is available to be patched/pumped out and/or is reachable from dry land. The cabling method was attempted on the wreck of the Mary Rose, which sank in 1545, but was unsuccessful due to the ship's resting in soft clay which would require cables to be passed under the ship, impossible with the technology of the day. The cabling method was used successfully to raise Vasa between 1956-1961, which is obviously quite a bit later than your example.

In between those two options, of course, is what to do if you want to retrieve small items scattered on the seabed -- either local divers or people using a diving bell could retrieve some amount of material, or at least put it into a bucket for recovery directly from the surface.