Welcome to PSO2 and PSOW, I hope you will enjoy your stay. Now, to avoid confusing you as a new player in this game with overly overly complicated systems, I will try to stick to each of your question as best as possible and not go much further.
Ideal Rod or Talis is a good weapon against boss, due to their potential, but FOTE end up requiring different weapons and skill tree for best possible damage, unlike other class. This is also true for techer and bouncer. Havin a weapon for each elemental attribute is called having a "rainbow set". For FOTE, before 13* you actually want to pick a weapon's element according to it's potential, so you would pick one with a fire technic potential (16% at pot3) with 50% fire element, etc.
Raw Tatk is one thing, but it need to be backed up by a good skill tree, since PSO2 rely more on stacking multiplier to high heaven (they multiply each other instead of being added together). Spare skill points at the end can be spended on Tatk if nothing better is advaible.
Here is a good skill tree simulator, which include mag and level cap class bonus. You can use it to plan build, extra tree for FO and/or TE if buy them using AC (cash shop). I would recommend 1st recreating your current build to see if there is some problem there that affect your damage. I can tell you from experience back in late EP1 and most of EP2 that a generalist build is pretty bad for FOTE, since a specialist can usually squeeze out more damage on even mob that aren't weak to the element spec'ed.
Gear wise, most people use
PSO2 swiki with the help of google translate. It might be an headache at 1st (and technically always, since google translate can give you same weird wording), but it's always up to date. There used to be cirnopedia, but that was a database managed by one/few people and is now fully outdated outside of some quick copy-pasting for older stuff. To directly answer your question, the name you mentionned are mostly the top unit set currently or weapon. Unit wise, you want a complete matching set for the set bonus, since most prefered give 60+ X atk or all atk and PP or HP. Saiki is still considered a solid set due to it's set effect of 60+ all atk and massive 25PP and people like to craft it so each piece give more PP (I will come back to crafting later). As long as you do your featured quest, you can get "Key" for Bonus Quest, the tokyo one on a high level character can drop you the Saiki set. Entry level good unit set would be it's lesser cousin, Hiei, which drop from this quest also at all level (if crafted it can potentially last until XH). Main difference between the two once crafted is that Saiki give 25PP and Hiei only 10PP.
Weapon wise, Sega is giving us right now "Collection Sheet", which, once completed, guarantee you a 13*. The Sheet are time limited though. Right now, we have the Revolucio set, which is more on the mid range or maybe lower of 13*, but a good entry if none yet or to make a weapon for less used element (Revo sheet is around until start of august). The Ray serie is on the upper side of 13* and come with a great potential, but it require more work and a scheduled only EQ (ray sheet around until start of october).
This is becoming too long and gone off topic... moving on!
Affix wise, we got this
solid guide from Selphea and this
affix simulator. They might not be fully up to date, but they should answer all the basic, and froma quick look, the simulator seem to be only missing Odin's special affix. Your run of the mill FOTE usually start out with Elder Soul (30 Tatk and 3 PP) + Technique III (30 Tatk) + Spirita III (4 PP) as their affix of choice on both weapon and units. If you have issue surviving, there is no harm in affixing Stamina III (50 HP) and/or Ragne soul (30 Tatk and 20HP) on units. Most people agree that at least having a relevant atk soul + Stat3 for 60 Atk with a balance of HP and PP that fit your playstyle/skill level get the job done. At higher skill level and budget, more Atk and PP is favored.
Tech crafting wise, unless you're willing to spend a large amount of time and ressource, it's best to request the craft you want to be done.
This old post from LonelyGaruga is a good start, but I would sure make to read the following 1-2 pages to see further reasoning or change made to the list he had made in that post.
Cirnopedia's page on Tech Crafting has the extra info for the most part. Since crafting has barely been touched since the last time that database was updated (pre EP4), it's still somewhat relevant. The only new stuff is some PA's craft, some technic alter'ing craft to Zonde and Nazan (unlike the rest of the tech recipe that simply adjust number) and the fact that crafting weapon is not advaible for Summoner's Tact, New Type weapon (or NT) cannot be crafted eitheir, and it's mostly reserved for "Red weapon" (potential is 14%-16% damage boost if the weapon is crafted), a common drop exclusive to VHAQ quest type (SHAQ got blue weapon, which doesn't have a potential).
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Managed to survive this wall of text? Then one last thing, make sure to get your Compound Technic, mostly Fomelgion (fire+dark long range laser cannon) and Baranstion (light+ice close quarter sword barrage). Those are excellent bossing tool, which work on a shared meter builded from technic damage you deal (multi hit aoe tech on large group usually build it very fast). During EP3, you had to complete a farming CO (client order) in ultimate type quest, but the npc is only advaible when playing on EP1-3 with the story advanced enough to reach EP3. Starting with EP4, they can be buyed from the Photon Sphere npc shop for 50 sphere each. You can get them with the recycle shop (10* unit x 5 or 10* weapon x 1) or the player market aside from farming.
As far as technic usage, rod vs talis and general/specific strategy is concerned, I will leave that for later or for a better FO player to answer.
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