There are a lot of ways to make a "gish" character, depending on flavor, desired armor use, martial-to-spellcasting ratio desired, and so on. Do you have a particular character background in mind?
Strength Patron Witch and Eldritch Knight is very strong, and can be done many, many ways. You can even have a Ley-Line Guardian Witch (spontaneous caster) who goes Dragon Disciple. Witch gishes have a very unique flavor from having Witch spells, and from using Witch Hexes for utility (not for normal hexing).
Anything from dex-based scimitar flurry to strength-based TWF and claws to archery-and-rapier can work.
Spontaneous Gish
Bard 7/ Dragon Disciple 4/X
Use a Longspear and poke things with you Attack of Opportunity while supporting your group.
Sorcerer 6 or 7/Dragon Disciple 4-8
With favored Prestige class and Prestigious spell caster, you can keep being a full caster while grabbing what you need to be a proper blaster and have good melee capabilities in the mid to late game. I really like this build now and is good for being a caster with some good defenses.
Strength Patron Witch and Eldrich Knight is very strong with a unique flavor. Ley-Line Guardian Witch is spontaneous, and may even go Dragon Disciple. There's a million ways to build a Witch gish - and some really cool options.
Paladin/Sorcerer/EldritchKnight Gish is a charisma-hungry build. So if you want to make a Gish that you can get the most out of one stat...
Or if you don't want to be Lawful Good, you could instead go for Cavalier (Order of the Cockatrice) which also benefits from high CHA.
I personally made a Ranger/Sorcerer/EldritchKnight Gish, because I love me some skill points (and Rangers are more "light armor" warriors anyway; I hate to see heavy armor proficiency go to waste). It was fun. Plus since I did Ranger up to level 4, I was a 1st level divine caster and had an animal companion as well (usually a dog, whose scent ability helped me track, and locate unseen foes - I had to buy a few replacement dogs over the campaign tho).
You could also go Arcane Archer too.
To me a Gish is best with only a scant few offensive spells. Most spell selections are buffs and battlefield control.
For a really devastating melee gish with major style points:
Witch-Dragon Warrior
Inspired Blade Swashbuckler 1/ Strength Patron Ley-Line Guardian Witch 4/ Dragon Disciple 4/ ???
Dual Talent Human: 15/17STR, 15/17DEX, 12CON, 15INT, 8WIS, 9CHA
Traits: Fate's Favored, Magical Knack
1IB. *Panache* / +Weapon Focus: Rapier / Two Weapon Fighting
2LG.
3LG. *Hex: ???* / Quick Draw
4LG. [+1STR]
5LG. Double Slice
6DD. [+1AC]
7DD. [+2STR] / +Power Attack / Arcane Armor Training
8DD. [+1INT] / [+1AC]
9DD. [+2STR] / [+1AC] / Improved Two-Weapon Fighting
Between Divine Favor, Heroism and DD STR, melee rolls - even with two rapiers - are huge (use Effortless Lace, ideally). Damage from two high-STR swords running buffs and Power Attack is a shredding machine.
AC with DD, mithral kikko and DEX is strong. Ironskin makes it absurdly strong. Panache allows parry and riposte.
Further levels depend on intent; ideally move into EK for straight fighting power.
So you know, you posted your topic twice, so there are two threads going - the other is longer, so I'd go there instead of posting here. For Arcanist I'd probably use an Imperious Bloodline Blood Arcanist. Ask in the other thread if you want more responses or more details.
Sorcerer9/Inspire blade Swashbuckler1/Eldritch knight
Using beast shape or monstrous physique to turn into little stuff for high Dex.
Eventually Coral Capuchin
Depending on what you mean exactly by gish (is melee required? Do you need to cast flashy explosive spells or is buffing sufficient? Does it have to be arcane magic or is psychic, alchemy or divine acceptable?) there are almost endless possibilities.
e.g. 1: Human Brown-fur Transmuter Arcanist 6 / Evangelist 10. Take the magical lineage & wayang spellhunter/metamagic master on true strike. Your feats at level 6 are divine obedience, quicken spell, power attack and branch pounce. Exploits of Lepidstadt shifter and altered shifting.
The plan here is that you can turn into something flying and drop from above for extra damage (possibly with true strike to make sure it happens), or just turn into a lion and pounce them.
e.g. 2: Nagaji Fighter 1 / Sorcerer (psychic bloodline) 9 / Eldritch Knight 10. Feats of shield focus, mobile bulwark style, missile shield and shield brace. You're carrying a tower shield, full plate armor and a polearm, and you've decided to use them all at once, possibly while radiating lightning from the elemental aura spell. You can also zap enemies minds when you feel like it.
e.g. 3: Halfling Inspired Blade Swashbuckler 1 / Grenadier Alchemist X. Weapon focus (rapier), weapon finesse (rapier only), fencing grace, risky striker, extra discovery for feats, spontaneous healing, precise bombs, psychokinetic tincture and frost bomb for discoveries. No, you're not a spellcaster, but you look like one with your sword covered in fire or acid and ghosts swirling around you.
Mechanically your damage will normally come from fencing grace (max dex), risky striker and an alchemical weapon added to your blade. The swashbuckler's parry and psychokinetic tincture can help cover you from risky strike and generally being a light-armored character in melee.
If you want an uber Gish toon, look no further than Psychic Warrior or Eld Knight (1Fighter/6Wizard/10EK).
Substitute Wiz for Sorc if that's how you want to go. I personally prefer Wizard when going EK simply for the spellbook.
Edit: Paladin2/Sorc6/EK10 is also really good for a gish toon. Pump Cha and have awesome spellcasting and saves, make up for your AC/Hit/Dmg with items, true strike and Cleave or Vital Strike.
I know you said you don't want to go Magus, but Magus8/EK10 is pretty outstanding because EK+Spellstrike and Spell Combat is pretty nuts. Grab a Bastard Sword (because you can use it 1handed or 2handed) and dip 1 in Fighter for the proficiency. An EK with Enlarge Person and a Large-sized Bastard Sword with Greater Vital Strike at lvl 16 and spellstrike/spellcombat... May the gods have mercy upon thine enemies.
Psychic Warrior is probably my favorite Gish class though. They can do SO MUCH more than just combat, and in combat they crush faces. They get combat feats and some really cool powers that buff you straight through the roof. And as long as you have Share Pain/Vigor combo with a Psicrystal, you have insane survivability.
Gnome (with the Darkvision, Fell Magic (make sure Wis is at least 11), and Master Tinker* alternate racial traits) bloodrager (Undead bloodline) 1/sorcerer (Ectoplasm bloodline) 5. Use Entangling Ectoplasm for battlefield control, Ectoplasmic Reach to cast touch spells from 10 ft away, or rage and charge to cause the target to become shaken for 1 round on a hit. Take the Magical Knack (Sorcerer) trait to keep CL at character level and use the 3rd level feat for Arcane Armor Training (wear either a mithral chain shirt or mithral kikko). Go into the eldritch knight prestige class after one more level in sorcerer (retrain the Arcane Armor Training feat to Quicken Spell on gaining 5th-level spells and ditch the mithral chain shirt/kikko for a +x haramaki).
*- Obsessive in Craft (Weapons), of course; wielding a tetsubo that the character crafted (alternately, for more of a redcap/underworld feel, take Bond to the Land (Underground) instead of Master Tinker and use a scythe)
For a different option (not as melee-focused), a half-elf* swashbuckler (flying blade) 1/sorcerer (Starsoul bloodline) 5 with the Divine Fighting Technique (Desna's Shooting Star), and possibly Startoss Style, can afford to really prioritize Cha without affecting attack rolls and damage as much. You may also want to look at the Ricochet Toss, although you may not be able to take it for another couple levels. Again, Magical Knack and Arcane Armor Training, plus switching to eldritch knight after swashbuckler 1/sorcerer 6.
*- or azata-blooded aasimar
Oracle of Battle 1 (using revelation to gain all martial weapon proficiencies)/Sorcerer X/Dragon Disciple Y/Eldritch Knight Z
Use all of the wands!
I was going to suggest magus 2/wizard 8/eldritch knight 10 when I read the title, but the body of your post makes it the opposite of what you want! Hahaha!!!