Primer: Synthesis and Weapon Effects
One of the more customizable aspects of the RP is the weaponry. In most combat RPs, you have a single weapon throughout tge RP. In keeping with the spirit of Final Fantasy XIII, each player has six weapons they can customize and upgrade. Everyone starts with their Balanced weapon and can later find or purchase 5 more. The 5 additional weapons each have a focus. One focuses on increased STR, another on increased MAG, and the last three in your primary roles. Your Balance weapon has good stats at the cost of having no additional weapon effect.
When you customize the weapons, you should consider the weapon's name, Synthesis ability, and Weapon Effect. The latter two are found on the Synthesis tab on the spreadsheet. There are two sets of info on the Synthesis tab. The left set are Syntheses and the right set are Weapon Effects.
Syntheses can be on weapons or accessories. The more accessories/weapons you have, the better the Synthesis outcome. For example, if you have Physical Wall on your weapon and you have an accessory with Physical Wall (such as the Power Wristband), you negate 5 points of physical damage on every hit. If you have three items with that Synth, you negate 10 points, etc. So if you have everything with the same Synthesis (4 accessories and one weapon), you negate 30 points from every physical attack. However, in order to get any bonus at all from Synthesis, you need at least one accessory that shares the same Synthesis.
Weapon effects are simpler. Only weapons can have these effects. Some of them are negative (Like leadenstrike - slows down your ATB charge rate). Most are positive (like Attack: ATB Charge - recharges part of an ATB slot whenever you hit an enemy). Nearly every ability on that list has a second tier that's stronger than the first. Leadenstrike is weaker than Ironstrike (although both are negative). Improved Raise is weaker than Improved Raise II, etc. You are only going to request the weaker option. Once you upgrade a weapon to Tier 2, you gain access to the stronger option.
So to simplify things, I would suggest completely ignoring any Synthesis that has Affinity or Duration in the name. Those are less than useful, but are included because some accessories have them. That limits you to 10 options to spread around to 5 weapons, and your base weapon already has High HP: Power Surge. I'd figure those out first, then decide on the Weapon Effects. For Weapon Effects, a lot of them are specifically for certain roles. For example, you won't get much mileage out of Improved Guard if you aren't a SEN. In addition, you cannot choose ATB+ for any Tier 1-2 weapon. That is only available on Tier 3 weapons, but automatically comes with your Tier 3 weapons.
I've mentioned Tiers for weapons a few times, so I should probably introduce the Weapon Upgrade system as well. This will come up later on in the RP, but once we get to camp, an NPC will be available to upgrade our weapons for us, as well as make other weapons with the other effects. Upgrades are progressively more expensive. Your first upgrade costs 5,000 gil and increases the stats of your Tier 1 weapon. The next upgrade is 10,000 gil, etc. Once your Tier 1 weapon is upgraded to level 10, you will be able to turn in a specific catalyst to upgrade your weapon to Tier 2. This catalyst will likely be the result of a quest, but it might be available in a store. The process continues until your Tier 2 weapon reaches lvl 20. At this point, you can get a Trapezohedron to upgrade your weapon to Tier 3. These are extremely rare and will require a very difficult quest to obtain one. Once you upgrade your weapon to Tier 3, you unlock your final ATB segment and are done upgrading that weapon. Upgrading weapons is extremely expensive, but also extremely rewarding. You can increase your stats a ton through weapon upgrades, but keep in mind that the group shares their gil and will likely want to upgrade everyone about equally.