Returning SMN having some questions about the gear.

[Havenchild]

Weapon: High Allagan Grimoire / Book of Spades
Head: High Allagan Mask of Casting w/ Evenstar Bootees or Eventar Hat w/ High Allag
Body: Evenstar Coat
Hand: Evenstar Gloves
Waist: Evenstar Sash
Legs: Evenstar Tights
Boots: High Allagan Boots of Casting w/ Evenstar Hat or Evenstar w/ High Allagan Mask
Neck: High Allagan Choker of Casting
Ear: High Allagan Choker of Casting
Wrist: Evenstar Armillae
Ring: Evenstar Ring
Ring: High Allagan Ring of Casting

Accuracy for Coils t6-t9:

t6 471
t7 481
t8 491
t9 491

First and for most this is not a summoners BIS set.

The truth of the matter is, after you hit the over 500 crit threshold, Det > Crit.
However I recommend always trying to be over 520 Crit whenever possible.

http://ffxiv.ariyala.com/N56R

This is the true BIS set. The belt would be the ONLY item you should swap out (if your feeling luckier with crits). You can hit T9 99-100% with 483 acc. Personally for me, Garuda may have missed once in like 6 weeks of T9 runs. The difference is pretty much negligible. The difference between the belts will ultimately be 1% Crit rate/ 1% ACC vs 13 Det/13 SS.

Please stop making full Int builds and calling it BIS for Summoners. It's completely misleading and untrue. There is absolutely no full INT build that is actually BIS on SMN after patch 2.3. You will get out damaged by countless other summoners who don't do full INT builds.

What about the Syrcus tower, which item should I get first ? Not the chest 'cause I'll buy the Evenstar one.

I would honestly recommend the Belt, if you don't immediately need the accuracy. Otherwise its a toss up between the Gloves, Boots and Belt as the most beneficial, depending of course on how much crit you have.