If the idea is to make it like a dragon, I would start at looking at the feats big dragons typically get and work from there.
i would consider both of these
improved natural attack.or
in that order if you want to get both of them.
Except you get an evolution thats twice as strong as Imp. Natural Armor, and Imp. Natural Attack is extremely weak for characters with multiple natural attacks.
A general advice for Eidolon feats is to shore up it's weaknesses like bad saves. You normally don't need to improve an Eidolon's offense, apart from the standard Power Attack.
Good feats for a quadruped Eidolon that dragons tend to have would be Iron Will and Improved Iron Will, Power Attack, and Improved Initiative (you get Multiattack for free).
The damage increases are rather small unless you can get your eidolon pretty big.
At medium size, the feat and the evolution would each add +1 average damage on two of your attacks. With Large/Enlarge Person, average of 2.25 damage for each.
If you compare that to Weapon Spec or even the Martial Focus feat (which would provide +1 to all the Eidolon's attacks), and you see how weak those options actually are (i.e. less than a feat).
For the evolution, it can't even hope to compete with evolutions like Ability Increase, Energy Attacks, or Bite. And since he (presumably) uses evolutions for stuff like wings and breath weapons, he doesn't really have evolution points to spare.
Weapon Finesse is generally a good choice for a Serpentine Eidolon at low levels. If you made you eidolon a skill monkey, Skill Focus and/or a +2/+2 skill feat for its specialty skill may prove useful. Of course, you won't get the full benefits of these feats until your summoner reaches 13th level (and thus your eidolon has 10 hit dice).
I'd consider Dirty Fighting, and then using that to make a combat maneuver build. A trip build is tempting as you can scale the eidolon up to competitive sizes, and use the high number of attacks to make trip attempts.
I would second Combat Reflexes once the eidolon's Dex gets fairly high.
I'd love to hear fun suggestions for a 3rd level feat. No good ideas for my tiger. Has power attack already, and I don't plan on ever getting reach, so combat reflexes is at best so-so.
Presuming you are playing an APG Summoner with a quadruped Eidolon, then Iron Will. Not exactly the most flashy feat, but failing will saves all the time isn't fun, either and your base will save is abyssmal. It's not so much domination (Outsider type, Devotion at level 6 and the ability to dismiss the Eidolon as a standard action help in that regard), but there are many other Will saves that you really don't want to fail. My current Summoner's Eidolon has both iron Will and Additional Traits -> Deathtouched (+2 vs. mind-affecting effects).
Regarding your list: Rending Fury is nice, but only if you don't plan on getting 4 claw attacks later. Nimble Moves becomes mostly obsolete at level 10 (that's when the Summoner gets Overland Flight which he can cast on the Eidolon). Eldritch Claws is mostly irrelevant with either Magic Attacks evolution of Greater magic Fang, unless you really need the silver part.
Noxious Bite sounds really cool for what the OP is planning - the DC isn't two high, but two free (in terms of action economy) attempts per round to instantly take the victim out of the fight is very strong. Might be worth getting Ability Focus for your breath weapon if you're mainly fighting living targets, too.
