Well for AV soloing and Farming I would say FM is the Way to go. FM gives you a great ST attack chain with Incinerate>Greater Fire Sword>Cremate>Fire Sword. This attack chain doesn't take much to get and is very good. For farming you have Fire Sword Circle which is a great AoE and kills fast.
"All right, they're on our left, they're on our right, they're in front of us, they're behind us...they can't get away this time"- Chesty Puller US Marine Corps
DM/Inv would be great for what you're looking to do. First of all, you'll be fighting lots of enemies which means saturated soul drain and invinc. If you have the vet sands of mu power you can pretty much perma shadow maul. And DM's heal makes you even more sturdy. And you'll be stacking to-hit debuffs on the baddies to add to your inv def.
Fire/Inv will do lots of damage too, but give no benefit to the specific situations you're aiming for and offers no additional mitigation. But like DM, it does high damage that is lightly resisted, and does have better aoe abilities. This would be my second choice.
DB/Inv does lots of damage, especially with insane recharge, and has slightly better mitigation than fire, but like fire offers no advantage in the situations you are aiming at like DM does, and on top of that, deals the most resisted damage type in the game. This would be my last choice, but DB is a very fun set to play if you're not worried about being slightly behind in performance.
I'm happy with my DB/inv performance while farming, using the Sweeping/Sweep combo.
It's good for AV soloing - but not so great as DM or FM would be.
On the other hand, being able to slot 2 -res procs as compared to none for these other two primaries can make a bigger difference teamed, especially if your team is light on debuffs.
Overall, I'd go FM/inv for the reasons BrokenPrey listed. An attack chain that does over 200 DPS and doesn't require much recharge, and Fire Sword Circle for AoE on top of that.
ok, so it's important to note that there are no bad primaries for scrappers. And as you mentioned three sets;
Dark Melee - It's mostly single target, but they are rapid attacks, and soul drain gives a very nice bonus, farming large mobs is probably not such a good idea, but if you find a place with big Bosses (ie north RWZ) it would be very powerful (on account of Siphon Life, which is very definitely awesome) and AV soloing (at least against non psi opponents) will be a breeze.
Oh, and Shadow Maul isn't at great as you may think (comparable to Sands of Mu), but Smite and Shadow punch still have that 'buzzsaw' attack quality, and the +End recovery of Dark Comsumption deserves special mention
(My most recent 50 is DM/Inv, and her survivability is ridiculous)
Fire Melee - has slightly better AoE than DM and more damage (at least on a low to mid cost build) but lacks the other bonuses of DM. But what it is is very pretty, you will want Aid Self if you want to take this and AV solo reliably though.
Dual Blades - Has a few problems compared to the other two, yes the combos add value, and yes, they're very pretty (especially with a cape and Hover on) but Smash/Lethal is the highest resisted damage type in the game, it lacks Dark Melees secondary benefits, and lacks Fire Melees sheer damage. It also requires that you take pretty much every power in the set to see it's full benefits (the combos)
none of these will make for as good a farmer as, say, a Spines/dark, but they could all be used for it if you're prepared to find the right targets (Fire melee excels on the Demon Farm, for instance)
All of them *could* solo an AV , but DM/Inv will have the easiest time of it with Fire Melee probably rating second.
and in terms of just plain pretty, well Dual blaes and Fire Melee are two of the prettiest sets in the game (Dark melee is kind of ugly unfortunately)
On a personal note, Dark Melee is my favourite though, even if the above doesn't sound like it, mainly because of it's huge secondary benefits. I do love Fire Melee to, and am in the process of leveling one (mid 30s currently, only basic IOs currently) And my Dual Blades wielder has been abandoned for some time, I know there are people who love it, but it really is the weakest straight out of the box, and by the time it matures averything you face has strong smash/lethal resist anyway.
Anyway, that's my five cents, if beauty is a key component here, go Fire melee, (your final build will be tighter, on acct of aid self, if you wish to hunt AVs)
But DM/Inv is very awesome and chock full of win.
I'll preface this with saying that I like farming. A lot. Something about being surrounded by big groups of Lts or Bosses and just methodically wiping them out is awesome to me. With that being said, I've already got an Elec/WP Brute and a Claws/DA Scrapper that seem to do pretty decently at that niche. Well, and a Fire/Kin too, but I prefer my melee.
The two sets I'm most interested in are DM, FM and DB. I know DM isn't exactly an AoE set but I like the idea of maybe looking into AV soloing and, while it's not FoTM DM/SD, I think a S/L capped DM/Inv would be a good pick for that. Plus, Shadow Maul would help me take those groups out at a somewhat decent pace. And having a heal in Siphon Life is a great addition to /Inv. DB, I like the idea of a Sweeping Strike/Sweep Combo AoE chain (I believe) and Nihili has been an inspiration for this combo. FM is a set I haven't played at all and looks pretty good, I'm just wondering about the lack of mitigation and if the extra damage is enough to carry the powerset.
So, I'd like opinions. Farming, general play and AV soloing will all be considerations and I honestly can't say at this point which consideration counts for the most right now.