Is this a good ship or not?
Honestly, not really. It's got plenty of good points, but that thin shell drags it down, as does poor bracketing ability. That said, it's not quite the deathtrap many people portray it as. Use it right, and you can get a fair amount of utility out of this ship.
At 4/6, the Agamemnon's speed is fairly average for a modem IS cruiser(it exactly matches every other House cruiser save the psychotic Kirishima), though against the ex-SL Clan ships it was likely built to counter, it would have an advantage, especially against the ponderous Cameron, Sovetskii Soyuz, and Aegis classes that make up so much of the invaders' fleets. Given the amount of Blakist assistance went into these ships, I'm pretty sure more than a few minds were also envisioning taking these vessels against the Com Guard Navy, even if the planners in question weren't the Agamemnons' legal owners. This speed advantage lets you dictate the range, outmaneuver your opponent if the fight gets close, or match maneuvers while keeping some thrust in reserve for ECHOs.
Fighter and DropShip capacity is decent, enough to provide your own escorts, though you'll need more if your Aggie is going to be leading a task force. In terms of fighters it carries more than the Avalon or Kirishima, but less than the Feng Huang or Mjolnir. DropShip capacity is similarly middle of the road, having more than the Kirishima, matching the Mjolnir, but falling behind the Avalon and Feng Huang.
That armor...ugh. Don't take hits. If you do get hit, don't take more hits to the same spot. Sounds simple, but given the lack of terrain or movement mods in space, you need to use every little modifier you can get. Angle of attack mods, evasive maneuvers, ECM...you need to use it all, even at the expense of your own to-hit numbers. My advice is to put a rank coward at your helm, and tell him he can fly however he wants, provided he keeps target X at least within the long range bracket. If his piloting skills are as strong as his self-preservation instincts, you just might last a lot longer than most people might expect. It goes without saying that the Agamemnon ranks behind every other House cruiser in this category.
The guns are a mix of good news and utter disappointment. They come *this* close to making the Agamemnon genuinely scary(even with the armor problems), but lets us down in just a couple subtle yet significant ways. Total firepower is VERY nice, with a solid mix of heavy and light capital guns that can do real damage at any range. The Aggie actually makes it to second place in our cruiser lineup here, with only the Mjolnir packing more heat, and even that monster is at a notable disadvantage at long range. Even better, you've got the heat sinks to use those guns, only needing to drop a single firing arc per turn to stay under your limit. While being surrounded may seem like a very bad idea, it does mean that incoming fire well be spread around all of your armor facings instead of concentrating on one or two and punching through that much more quickly. While I still wouldn't recommend getting in close with enemy WarShips, this can be of great use when facing a swarm of DropShips and fighters.
Now for the bad news. While you've got long-range firepower galore, most of those guns are mounted in twin turrets instead of triples or quads, so you can't bracket that well, thus limiting the full potential of your firepower. Most of the other House cruisers are also poor bracketers, but Star League-vintage ships may very well peck you to pieces while range penalties are making several of your shots fly wide. To compound this issue, the NACs that are the bulk of your armament have limited ammunition bays. The 30s only have ten rounds per gun, and the triple-20 mount in the aft quarter that is your most reliable damage-dealer only has 16 shells per gun. You're encouraged to fight from long range, but your accuracy is going to be spotty, and you can't afford to spray and pray from back there lest you run the guns dry. You're also completely lacking in capital missiles, so you can't use bearings-only shots to try and score some equalizing crits. On the upside, your extensive point defenses mean the odds of someone doing this to you aren't very good either.
Needless to say, an improved gunnery skill on an Agamemnon is worth its weight in gold, despite the astronomical BV cost you'll be paying for it.
Back to some good news. In terms of anti-fighter defenses, you're actually doing fairly nicely. Having a sizeable capital laser battery, solid 4-point can opener and a pair of 2-point crit seekers in each arc(and as above, the heat sinks to use almost all of them at once) means that no fighter squadron that makes it past your screen well emerge from an attack run unscathed, and several may not be in any condition to try for a second run. I would have liked more 2-point bays, but overall things aren't too bad.
All in all, I do have to rank the Agamemnon at the bottom of the House cruiser lineup, but not THAT far below everyone else. If you're taking an Agamemnon into battle the odds are not in your favor, but defeat is by no means assured. And even if you do go down in flames, the odds are actually very good that you'll leave the other guy with one hell of a repair bill.