For an archer, transmutation might be best. Reduce Person, Cat's Grace, haste, Fly and Greater Magic Weapon are all great aids for an archer. A baseline might look something like this:
Wizard1
Wizard2
Wizard3
Wizard4
Wizard5
Fighter1
Eldritch Knight1
Eldritch Knight2
Eldritch Knight3
Arcane Archer1
Arcane Archer2
Arcane Archer3
Arcane Archer4
Eldritch Knight4
Eldritch Knight5
Eldritch Knight6
Eldritch Knight7
Eldritch Knight8
Eldritch Knight9
Eldritch Knight10
This would give you +16 BAB, 9th level spells etc. But as most campaigns doesn't go all the way till level 20, you might want to change it up a bit. Fighter4/Wiz2 lets you enter Arcane Archer at level 7, but your spellcasting will be hurt.