Unless you have connections with other players, the transporting of goods for isk come down to a few options:
Distribution Missions - Theses donGÇÖt pay much in LP or isk but you are getting paid to move stuff. While not a great source of income, it is not a bad idea to check your agent finder for them if you are just looking to GÇÿfly around emptyGÇÖ. When I get bored I sometimes will grab a hauler and wander the space lanes taking random distribution missions.
Trading. GÇô You buy stuff at one place for cheap and deliver is somewhere else to sell (for profit). You need to be good at math (not great, just good enough to know how to calculate a 5%+ profit margin or your unskilled noobness will be throwing away money on taxes just moving stuff. Although often out of date, this site
http://eve-central.com/home/tradefind.html can give you examples of things to look at trading as well as potential profit.
Courier Contracts GÇô This is a contract where you will put down collateral and be given a package to haul within a certain timeframe. This is a player-created contract. I repeat, this is a player-created contract. Some are completely legit, some are blatant scams, some are subtle scams.
A legit one might be move 200,000m3 of stuff from Amarr to Jita for 200,000isk. There might be a 5 million isk collateral. So you would pay 5million isk to pick up the package and you would get back your 5 million isk plus 200,000 isk on delivery. If you fail to deliver because youget blown up, get there late, just canGÇÖt get there you donGÇÖt get paid and you donGÇÖt get back your 5 million isk collateral (the other guy does).
Blatant scam contracts will often have you flying somewhere you cannot go, like an outpost in 0.0 space. These will usually have small cargos, huge payouts, and semi-huge collateral. You take the package and fly to where you are going but cannot deliver and therefore lose your collateral.
A common thing with scam courier contracts is also to make them so large that the only ship to move them is a freighter, which is then ganked by a suicide squad so that they can keep the collateral (which was much higher than the cost of the lost ships).
A subtle courier scam runs along with something called margin trading. This one is interesting because you, as a player, can look at the contents of a courier contract. So long as you donGÇÖt unpackage the GÇÿplastic wrapGÇÖ you can see what is inside. What ends up happening is this: You get a moderate level courier contract (10 million isk) and there is one item in the wrap that happens to have a buy order on the market for 20 million isk (but only one, or with a minimum quantity higher than what is available). You break the package and try to sell the item (you lose the 10 million isk collateral, but can sell it for 20 million right? Wrong). The person buying the item doesnGÇÖt have enough isk in their wallet to pay you so the order drops and you are stuck with a 10 million isk paperweight.
I will point out though that some players legitimately put stupidly low collaterals on their courier contracts and then discover that their cargo will get stolen. A friend of mine found a contract to move a Maelstrom hull to low-sec, the collateral was only 2 million isk. He now has a new Maelstrom.
In terms of ships, anything that can haul can be used. You will want to consider things like:
Astronautic Rigs GÇô Small (Frigate and Destoryer) or Medium (Cruiser, Battle Cruiser, and Industrials) Cargohold Optimization I (the tech 2 versions are stupid expensive) which only requires the skills Jury Rigging to 3 and Astronautic Rigging to 1. These increase the cargohold size of your ship.
Expanded Cargo Hold II (there are lesser ones, but the skill needed for tech 2 versions is Hull Upgrades 2GǪ half hour of training) these go in low slots on you ship.
Giant Secure Cargo Containers are 3000m3 in size and can hold 3900m3 of cargo. They require Anchoring to level 1 (8 minutes to train).
Since you are Amarr the ships you might want to look at for cargo space are:
Frigate: Magante
Destroyer: Coercer
Cruiser: Augoror
Industrial: Bestower
Hope this is both a help and a warning.