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The Alchemist is a real diverse creation, but ultimately boils down to two roles; Physical or Ranged/Explosives. The Alchemist itself is a very squishy person up in the front lines all by himself, he's not like the fighter, paladin, cavalier, or even battle druids who can go in there and take a beating. Monks have so many feats to help them compensate for a lack of armor and BAB compared to the harder hitters.
This might sound really stereotypical and closed-minded concerning this class, but in order to be efficent most people choose either the Mutagen/Extracts or the Bombs/Extracts and then grow from there.
I do not have as much experience as a Mutagen Alchemist, but what I can do is show you the more...explosive side of Alchemists.
Bombs are one of the many new things that were added into the expansive field of the alchemist. Without this and the Mutagen, this guy would really just be a Rogue without any sneak-attack bonuses and who could cast a few spells. Bombs are a great conjunction with the Extracts themselves, as both are modified by the INT modifier, which certainly makes their lives a lot easier to know what stats to modify first.
Usually, I like to order them as such: INT, DEX, STR, WIS, CON, CHA
INT and Dex are going to be your heavy hitters here, as INT is the staple on what most of the things a Bomber is going to be focusing on getting the most out of. Dex is there because, let's face it, you're NOT going to have a ton of bombs everywhere, unless you're planning on using 8/11 feats on just the Extra Bombs feature, and the next best thing for you is a bow or a crossbow of some kind. Str is for damage and carrying weight, although it and Wis can be interchanged in terms of importance, just remember that it's good to have SOME points in there to help you out. Con is ok to have, but keeping it at a neutral level won't really kill you to much if you just stay out of the main brawl. Cha is a dump stat for this one, sure Use Magic Device would be pretty nice, but most teams come equipped with a mage already so you can just toss whatever YOU can't use to them.
For a normal 20 point game...
STR: 14 (+2)
DEX: 15 (+2)
CON: 10 (0)
INT: 15 (+2)
WIS: 14 (+2)
CHA: 7 (-2)
This gives you a decent balance of what the Alchemist wants and needs in both offence and defence. The Wis boost also really helps his weak Will saves, so you won't be as much of a burden to the team when some mind-altering magic tries to get on your butt. This is without any racial modifiers, and can be tinkered around with a few more points. In reality, you could easily take down either the STR or the WIS modifier to 12 and then increase the INT towards 16, or 17 if you want to sacrifice more, all I have to say is be wary about how you approach how much you give and take away. Take to much away and your alchemist might not be as effective, but to much in and it might have to many things cluttering it.
For races, the best ones to use are by far Elves. If your GM will reccommend it, Teiflings are the better option though, as you get the same bonuses but instead of the cost of CON, it is replaced with CHA
Here's an elf using only the pre-build I just gave
STR: 14
DEX: 17
CON: 8
INT: 17
WIS: 14
CHA: 7
Again, not bad. Might sacrifice some points from STR or WIS into CON but still it's not a bad choice..
Teifling with the same pre-build:
STR: 14
DEX: 17
CON: 10
INT: 17
WIS: 14
CHA: 5
Lookit! nice an neat, but jimminy crickets look at the size of that CHA...it's kinda scary how bad it is...
Other races to forward towards are the Half-Elf, Human, and Half-Orc. While these only give just one +2, they make up for it with traits that could really help in the long run! Humans and Half-Elves sorta do better than the Half-Orcs though, but if you wanna, then don't let the man get you down, man. Halflings would be OK, if you didn't want such a poor CHA stat, although that'll result in a shorter STR. I wouldn't even try Gnomes or Dwarves. Although the Dwarves are nice, they really don't add onto what Blasters are good at.
For feats, focus on all of the more long range ones. Point-Blank and Precise being YOUR ABSOLUTE FIRST. I'm still a bit of a newb at all of this, but if it's one thing I know, it's that these things are going to be your best friends with any long-range person. Rapid Shot, Manyshot, and Deadly Shot should also be in that list as well, since the crossbow is going to be your biggest helper when your bombs are all said and done. A few Extra Bombs feats are fine too, as long as you use them in a decent pattern with other long-range feats and weapon specialisations.
Discoveries are a bit more self-explanatory. The bomb discoveries even more so, with most of the discoveries just changing what element the bomb makes when it goes boom. The two I'd like to point out though are Precise Bombs and Fast Bombs. I believe that Precise Bombs are going to always be your number one choice when making the Blaster Alchemist. It definately helps when you throw an explosive in your friends' way just to get to that troublesome enemy and have them not be affected by that splash radius. Fast Bombs will deplete your bombs a bit more, but it'll definiately begin to show it's prowess on the 8th level when you can get it. For the rest of the discoveries, I say just go crazy go nuts about picking. But there are two more that I'd like to briefly mention, however and that's the Extend Potion and Eternal Potion mix. In a nutshell, think about having a PERMANATE HASTE on yourself...yeah, enough said.
I hope I helped a bit...also I hope someone knows a bit more about the Mutagen class to help you out with that...oh and here, let me get this thing back on *glues your ears back on*