Relevant abilities (From Blood of the Beast)
At 1st level an Ancestor subtype Eidolon gains the racial traits (no alternate traits) from the Summoner's race (not sure if this includes ability adjustments).
A 4th level it gains the sorcerer, fighter or rogue simple class template as though it had 1 HD (but can't have abilities a level 1 member of that class wouldn't)
At 12th level those advance to be as if they had 5 HD.
Biped only naturally makes the ancestor favor weapon wielding builds. For this I think the best race is one with proficiencies or Human (who can blow the bonus feat). If Half-Elf (and their ability to pick human stuff, elf stuff and half-elf stuff) lets you pick one of the three, they are likely the best.
Spells will only be level 1/2 and an Eidolon is (sorta) full BAB so it would seem like typical Gish pick, but the obvious ones can be cast on the Eidolon either directly (Mage Armor) or via Share Spells (Shield) so the longer duration ones seem like they should be skipped. Thunderstomp seems an option, as you can still use Strength and BAB if you want to, as does Longarm (Being huge means huge reach. Being huge and having Long Arm means huger reach). Prehaps Extra Traits (Magical Knack/???) and Pearls of Power would be worth it for them?
Bloodline though I have no idea what to pick. Most Sorcerer Bloodlines don't have good 1st or 3rd level abilities for a gish.