good news / bad news time...
good news! just about everything in abyssea can be done effectively with 3 characters and the right mix of jobs.
bad news! dragoon is not one of those jobs... like ever.
the "ideal" setup will vary depending on what you're doing, but it will generally be made up of some combination of NIN WAR WHM BLM MNK and THF
lemme give you some context now that i've kicked your favorite baby down the stairs. (sorry, it's not my opinion, it's my observation)
abyssea basically revolves around it's proc system, which is divided into 3 categories: red, yellow, and blue.
- Red procs guarantee the drop of key items.
key items in aby are hugely important, they include atmas, abyssites, and the pop items for higher tier NMs. Red procs are inflicted via elemental weaponskills like seraph blade, raiden thrust, shadow of death, so on etc. all "RED WSs" are relatively low level. low enough that a warrior can learn about 90% of them, everything except dagger, katana, and great katana. (that's where the ninja comes in) so while building pops, or hunting for atmas/abyssites, the "ideal" low man setup is NIN WAR and WHM
- yellow procs hugely increase (but do not necessarily guarantee) the drops of emp armor items.
seals for +1, and assorted stones, cards, coins, and jewels for +2. Yellow procs are inflicted via magic. most mage jobs bring some yellow procs to the table, but the overwhelming hero job here is BLM. BLM has about as many yellow procs as every other job combined, and if you really wanna get crazy with it they can even sub BRD to pick up that entire line as well. (elemental seal will make them land even with sucky /BRD skill) then when you consider your tank (NIN, or even THF/NIN) and your healer (WHM) already bring a handful of their own yellow procs, a 3 man team of NIN WHM BLM is excellent for farming your armor. (though +2 NMs are almost always key item pops. ideally you build the pops with a war and have him swap)
- Blue procs dramatically increase (but do not guarantee) equipment drops.
MOST of the stuff you want out of aby is not dropped directly as 1 whole thing, it's pieced together from seals, stones, or is an emp weapon, but there are notable exceptions, and this is how you get them. Blue procs are also inflicted via weapon skill, but from a very different pool. "Blue WSs" are all physical, and generally higher level than red. rather than being broken up by element, they are broken up by type. blunt, piercing, or slashing. you can control which category you get by spawning the NM at a certain time. the hero job here is definitely MNK. MNK alone learns ALL but one of the blunt weaponskills, and that one MNK is missing WHM can learn. (hexa strike) a good monk can tank fairly well in aby, so eventually you will be able to do most of your blue procing with just MNK and WHM. in the meantime your trusty NIN can tank, or you could use a THF for treasure hunter. (never hurts to have more treasure hunter)
the last thing you'll do in aby is build emp weapons. the items to build emps are always dropped off higher end NMs, so you will need to build the pops using red weakness. (the old NIN WAR WHM setup) but once you actually have the pops, the WAR isn't all that important. emp weapon items themselves are not affected by any procs, so swapping the WAR out for a THF is a decent move, though not required. they ALWAYS drop 1, TH will help you get the 2nd sometimes, but if the war helps you kill significantly faster, well... up to you.
i know this is all gonna come off as kinda dickish, and i understand every job brings something to the table here. blu has yellow procs... but only about 15% of them compared to the other 85% you can get without a BLU at all. is it worth bringing an entire 4th person? paladin is the only job with swift blade, a blue proc. but is that 1 unique proc worth a whole 'nother person? especially when you can mitigate the need for it by focusing on the blunt procs? just about every melee job has some red procs, but when you can get every red proc between 2 jobs, why bother with more?
i mean it sounds like you're already short on manpower as it is. if this comes off as a hard truth, i'm just trying to help you get the most bang for your buck.
overall i recommend you start out by getting yourself and all your friends the big atmas and abyssites. they're common drops, meaning if one of you gets them, you all get them. so it's very easy to team up with strangers if you have to. no competition for drops.
then try to get at least 1 zone boss win, to allow you to equip a second atma (the first can be purchased via cruor) and your +1 armors.
when you are ready to work on your +2 armors, start thinking about what emp weapons your group wants to make, all emp weapon NMs ALSO drop +2 items, and you'll be killing a lot of them to make those emp weapons. there may be a few good opportunities to kill 2 birds with 1 stone. even if you don't feel ready to make emps yet, if a +2 you need lines up with an emp you want, why not get your +2 there if it's an nm you can take?
once you have your +2s it's probably time to focus on zone boss and caturae kills so you can finish off the abyssea storyline and fight shinryu. this is where it's gonna get tough to lowman. but no shame in brewing a few here and there. i'm pretty sure that's what brews are for, the lowman safety net. they're crazy expensive until AFTER you beat shinryu though, so see if you can get someone to help you out; and you can "owe them a brew" later. (if you keep an eye out you might even be able to "leech" these wins. just like atmas, everyone in the alliance gets credit for the kill, so most people shouldn't mind you tagging along) 6 wins will allow you to equip a third atma, and shinryu himself has some decent gear and an excellent atma. once you have that you almost can't lose and aby is your playground. farm it to your hearts content. go back and pimp out those jobs you had to give up on earlier.
good luck man.