Using a manufactured weapon attack forces all natural attacks to secondary? Yes. It is on page 302 of the Bestiary. It is a general rule for all creatures.
Actually, APG RAW says bite can only be added once. If the creature already had bite, then the STR damage goes to 1.5x. UM RAW lets the bite be placed on a second head, but does not say the bite evolution can be take more than once (past the free one). So, by RAW, only two bites can be used. Then their Hydra example eidolon violates that thought, and puts one bite on each of the five heads. Again, Paizo fuzziness.
Poison is out for the moment, as it needs 7th level. Yeah, I missed Energy Attacks needs 5th earlier.
The Lesser Evolution Surge spell only gives you one evolution, and up to 2 points. So, you could add pounce or claws, but not both, without casting it twice. It is great for adding things like Gills or Climb, that are very situational, but needed when they are needed. After 5th level, winged flight is useful too.
So, with a little more explanation of what is important to the character,
2 extra head, 1 extra bite, 2 trip, 1 fire resist, 1 claws(fore legs) is the best damage potential.
2 extra head, 1 extra bite, 2 trip, 1 fire resist, 1 Imp Damage(bite), not optimal, 2 +1 avg damage vs 2 +2.5 avg damage with claws, but better for attempting to go through DR.
2 extra head, 1 extra bite, 2 trip, 1 fire resist, 1 Imp Nat Armor has the better AC.
2 extra head, 1 extra bite, 2 trip, 1 fire resist, 1 skilled(acrobatics) is the best flanker.
Since the eidolon can have four attacks per round now, the first is probably the best unless you don't want to be a showboat.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.