Since the eidolon is an NPC, you'll only be getting 1/2 it's HD in hit points (5.5 ish), so Toughness will be essential for that first level (and handy for the rest of them).
I prefer the quadruped, to be able to take advantage of pounce, and eventually assume a draconic form with wings and maybe a breath weapon. Elemental attacks, to add +1d6 damage to each melee attack, is pretty awesome, although you might want to think about what sort of elemental damage makes sense for your character, so that you don't end up spending four levels talking up your Eidolon as an immature red dragonling critter, only to discover that you're facing far too many fire resistant creatures and would rather take acid or electrical or cold damage for your elemental attacks. Leave some wiggle room in the flavor, so that you don't feel like you're abandoning flavor for mechanical benefit when you find it necessary to tweak your build in an unplanned direction.
That's a huge thing, being able to reshape your Eidolon every level, and take on abilities that seem like they will be beneficial in the direction the game is headed. Too tight of a 'theme' might make it awkward and 'meta-game-y' feeling to adjust your Eidolon in this fashion, and end up cheating yourself out of a valuable class ability.
I've seen some good use of the bipedal Eidolon as well, but they almost always end up having four to six sword-wielding arms and looking like a Hindu diety. The best use of bipeds was in early Beta when they could wear armor, and that's a thing of the past.
Except for the Iconic, Balthazar, and his chicken-snake-thing, I haven't seen a whole lot of love for the Serpentine body type.
The
grease spell is one of the best 1st level Summoner spells. Learn to love it. You'll end up with Spell Focus (conjuration) as a prereq for Augment Summon, so conjuration spells like
grease and
create pit and
black tentacles will have a bit more shelf life. The Summoner is pretty good at control effects, so you may want to do what you can to enhance that (carrying tanglefoot bags, caltrops and / or alchemist's fire to throw at people in pits or stuck in
grease can be fun as well, to add injury to insult). Summoners don't have a bunch of attack spells, and it's probably best to focus on buffs, debuffs and control spells.
Haste,
slow, etc. are great spells for your summoner and his allies (summoned and otherwise), while either the Eidolon or summoned monsters handle the DPS.
Don't be at all afraid of your Eidolon dying. The Summon Monster SLAs are amazingly powerful (particularly if you've got Augment Summons), and after some aggravation with how quickly the Eidolon ended up dying *in every single combat,* I came to see it as a blessing, as the Summoned Monsters are no slouch, and cast as a standard action and last 10 times as long as they would have if you were some lame conjuration specialist wizard.
Life Link was designed by committee. Your Eidolon won't die until it reaches -Con in hit points (13 or so), and, at 1st level, attempting to use Life Link to save it will leave it *still* at negative hit points, and you now at negative hit points yourself. You could, quite easily, kill yourself, and not manage to revive your Eidolon (which will disappear when you drop yourself unconscious trying to stop it from disappearing, perversely).
The language I would use to describe how wonderful Life Link is can't be used on a family-friendly website.
Note that the Eidolon does not have the empathic link that a druid has with his companion, and you cannot give it directions silently as a free action. Since it's relatively smart, and understands any language you speak, pick something rare or obscure to give verbal instructions to your Eidolon without announcing to the entire world what it's going to do in any given round. I tend to pick Draconic, but some elemental language, Infernal or Celestial all make sense, since you might need to verbally instruct summoned celestials or devils or elementals at some point as well.
Celestial and fiendish critters in Pathfinder do not speak or understand celestial or infernal/abyssal, and do not have Int 3, as in 3.5, so summoned celestial/fiendish animals are never going to be able to do anything other than attack the foe in front of them, which, thankfully, they do without instruction. Summon spells are *much* less versatile, due to this lack of any real control, than they were in 3.5. Don't expect to be able to summon a celestial monkey and order it to climb a wall and unlatch a second-story window, or climb a tree and unhook the snare-line that's got your fighter hanging by his ankle.
Nor are celestial or fiendish critters good or evil in Pathfiinder. They might be able to *smite* evil or good, but they have no alignment type themselves and remain neutral, so don't expect to be able to send your celestial dog to smite the enemy conjurers fiendish wolves, because the fiendish wolves are neutral wolves from hell.
