Grand Knights History

This is just going to be an information dump on general play.
First things first, it's highly recommended you play this if you can go online with your PSP (doesn't go through PSN.)
Second, there is a complete IP block on non-Japanese IPs, look up how to connect online through a proxy on your PSP, and even then your results are mixed.
Third, JOIN AVALON. (Inoue Kikuko mage nation)
I know ikemen Sugita is cool and all but Logress is way too overpowered right now.

Anyway, at its core, Grand Knights History is initially a lot about stat tweaking, and becomes purely about strategy in the end-game.
Think of basically versus Etrian Odyssey or 7th Dragon where you can bring up to 8 parties.

The way the "War" mode works is this.
In general you will always have one "Main" party, the one you are directly controlling.
But you can also set up limited AI routines for your other 7 parties.
Because humans generally should be able to beat the most well-crafted AI parties, human players are encouraged to fight multiple AI parties in a row for greater rewards (up to ten), all the damage and Brave lost is saved from the last battle so it is dangerous if you aren't prepared to handle certain types of AI parties.
Alternatively, you can stop your streak early to heal but get less rewards for it.
You can run around in a currently contested territory and just free PvP random AI or human teams (online and offline!, offline just saves a snapshot of the world state), don't worry if you lose because you're not affecting the actual front line.
Keep in mind the enemy parties you face will scale to your level.

Front line war for contested territories is separate, and is more or less directly decided by wins and losses for each side in frontline battles on a real time basis, losing here hurts your team.
Here's a rundown of a sample front line war phase.
1. I go to a location in the contested territory where a battle line is and attempt to beat ten (usually AI) teams in a row (that's the maximum streak you can have I believe, and stopping to rest takes valuable phase time.)
2. At the same time I have set up my other 7 parties for AI routines, hopefully enemy human players will meet them when trying to get a ten streak and are sufficiently hurt or damaged by them that they are forced to stop continuing their streak or die.
3. Occasionally I will meet a human party, though you never quite know if its human or not (some of those AI team setups are really well built).
4. The number of wins and losses are tallied on each side at end of phase, whoever has more Wins pushes the morale? nation meter at the bottom toward the enemy's direction.
5. Nation with more meter at the end of a certain number of phases wins that battle and the territory.

So that's online war, problem (or not problem) is right now there are tons of bad AI AND human-controlled parties, so in fact a lot of people are cannon fodder.
To become not cannon fodder you need the offline component.

I'd be lying if I said the single player for Grand Knights history isn't a lot of OCD stat tweaking and build testing.
Each party you make in single player mode has a "training" period of 60 days.
When the training period runs out you have the option to send your characters to the above "War" mode.
Sending a character to "War" removes them from the single player world, they are now permanently only able to online or offline PvP and are no longer able to return to dungeoning.
However it frees up a character slot, you can only have four active characters in single player mode at a time.
You actually want to send your first four characters to war fairly quickly (don't get attached), as they will suck.
Enemy stats scale way better than yours with level, and honestly the first party you make is going to get stomped, maybe even as soon as level 5 (if you can't figure out the system).
You can use quite a bit of strategy to get far with your initial party, but in the end you're going to reach a stopping point (mine was about level 20, way higher than usual for a first party).

What you want to do with your first party:
1. Maybe complete some of the storyline quests to unlock new formations and new locations.
2. Maybe level up some to unlock new weapons and items.
3. GET AT LEAST 13 TRAINING PERMITS.
4. Send them to war after the 60 day training period is over, unless you want to farm more training permits.
5. Try some offline or online war, you might even beat a few AI teams if you're smart, but be prepared also to lose to some hilarious setups or just outright better equipped and better statted teams, AI or human. Like four hammer wizards, or a team that spams multi-hit instant death crossbows, or a team that basically Don't Acts your entire starting turn. Because the teams of your enemies scale to your level, if you leveled quite high in story mode you're going to meet some later generation teams using training-boosted stats.

What you want to do with your second party:
1. Buy enough Brave recovery items.
2. Use the 13 training permits on your entire team and get Marvelous card spins for each character until the training period runs out.
3. Look at your stats, and realize you are still level 1.
4. What you have more or less is an uber twinked team of level 1s. You can send them to war and their stats would destroy any first generation team on level 1, but keep in mind that it's highly unlikely someone sent their first team to war at level 1. Instead you'll probably run into other similar stat boosted teams as yourself, plus none of you will have any skills besides the default so it's sort of a coin flip. Hold off for now.
5. Use your level 1 super team to do just story quests until you get the ability to leave the country so that you can unlock the entire map to find the shops that sell the highest offline non-war equipment. Your home country's store scales with your level so it will still sell garbage. Run from anything you can, and only fight forced battles that show up in story. Do not worry about Brave loss, to not have qualms about running out of Concentration, do not worry about returning home at any time (training period is already up.) Because enemy stats scale way better than yours, but you have a huge initial boost, you should be able to one shot any normal encounter with 1 AP skills (not that you should bother), and you should be able to win Story battles with very little difficulty (those golems at high level would normally stomp your face.)
6. Read the Min Max thread to get an idea of what you should be really aiming for. As said, while 13 permits is a wonderful cost efficient way to get a jump start on party two, those going for extreme stat optimization will either aim to farm at least 36 to 72 permits for their later war teams.
7. It's probably not worth leveling to 49+ to unlock the last two tiers of buyable offline non-war equipment, do that on a later fully optimized party...when you feel like going to war just send them up (preferably low level), masteries build much faster in war and you can start seriously unlocking the war only skills and being a real competitor (not cannon fodder) online. Make sure you have the desired amount of permits for your next party as always.

All the parties afterwards will be pretty optimized starting stat wise to your liking, so you should concentrate on making multiple viable war parties to fight online.
Also, you should probably delete your first party from War, maybe even your second or third if they are not stat optimized to your liking.
Do this only when you have something like eight War parties hanging around.
As always, experiment like crazy with your builds in War, there are good AI farming teams, there are good AI-controlled enemy player stalling/stopping teams, and there are good human vs human teams.

List of stuff to note:
In War there is a rotating list of skill bans for Auto-Battle, be sure to update your AI routines if it affects you.
The Support skill that drops all your AP costs by 2 after a Defend is godlike, and it only costs 3 support points to learn.
There is a Support skill that makes you dodge 100% for the first turn...it's up to you whether you think it is worth it. A lot of day 1 AI teams were running it on all four of their characters and royally screwing with new players.
There is also a Support skill that makes you dodge 30% for the first three turns.
Combined with the skill that gives you 1AP for each successful dodge (multihit attacks on multiple or single targets count as multiple dodges) and you can see some very powerful combinations here.
Just a note the 1AP dodge regen skill and the first turn full evasion skill were both sealed week one, along with instant death.
Speaking of instant death, it's an archer support skill that each attack can proc instant death. As mentioned before, multihit attacks count as multiple attacks so a very powerful AI-killing team was spamming multishot instant death crossbows.
Judgement is an all-hitting low damage spell that has a chance to paralyze. (random chance of not act.)
Mirage creates a 1Hit barrier for your entire team.
Drain Act drains one to three AP from your opponent but costs 4AP to use, you really need to two be effect but then you can cause lockdown loops if your wizards are fast enough.

New rotation of sealed skills is the two dodge skills, plus the Wizard doubleact spell.