Seconding Grenadier. Precise Bombs makes your party much happier with you, and you can use a bow rather than a crossbow with that free martial weapon proficiency. Bows just have better stats in PF.
The main next choice is which alchemist discoveries you're aiming for. Tanglefoot bomb is the fastest way to get some control but not the only one; Smoke Bomb followed by Stink Bomb is very effective, as is Glassfoot Bomb + Frost Bomb. These are mostly incompatible by the way, you can only use one discovery with a star following the name on any given bomb.
Some later discoveries you may want are Explosive Missile to extend the range of your bombs when necessary, Fast Bombs to be able to nova against a dangerous foe, and maybe Dispelling Bomb. There are a number of useful non-bomb discoveries too such as Cognatogen, Spontaneous Healing, Tumor Familiar and Infusion which you may want too. Later on you'll get Greater/Grand Mutagen or Cognatogen.
On feats if you're going to be doing a lot of ranged combat that will probably use up most of your feats. Point Blank Shot and Precise Shot are essential, if you're going to use the bow a lot then Rapid Shot, Manyshot and Clustered Shots will be good, if you're going to use bombs a lot then Extra Bombs and Extra Discovery will be good. Later feats may include Weapon Focus, Far Shot, Improved Critical, Impact Critical Shot, Improved Precise Shot, and maybe the Overwatch Style chain considering you're aiming at going to a high level.
half elf is a good race. you can switch out their skil focus for a +2 to your will saves (aka- the mind control and curse preventing save; aka scariest save). on top of that, half elves also get another +2 against the mind controll stuff.
overall, this would patch up the alchemist's poor will save, and it would give you room to use dex mutagens (dex mutagens lower wisdom, which is the will save stat)
otherwise, yeah- bomb stuff. i wouldn't focus too much om fast bombs, since it eats up your bombs but doesn't do much else on its own. nova is nice as an option(sometimes you just want a dragon to be a scaly crater), but running out of bombs means your build loses its main fun thing. just using bombs as a different set of spells aimed at bringing misery to enemies throughout the entire day is fine.
I agree that Grenadier is a solid choice, but I also think you should look at the Mindchemist archetype as well. Extremely solid bomb damage, and the added bonus of doubling your INT bonus to Knowledge checks. Tiefling is a good choice for race with the Dex and INT bonus.
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Fast bombs to Nova,
Force Bombs for unavoidable damage
Healing Bombs for healing utility (nice when combined w/ Fast Bombs)
I wouldn't spend a discovery on Precise bombs, actually. Just drink an extract of Targted Bomb Admixture so your bomb adds twice your INT to damage, but only targets a single person. Works especially well with Cognatogen active, which you can get for free with the Mindchemist Archetype (also gives you Perfect Recall for twice INT to knowledge checks--always a good thing).
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Oh, didn't notice you were looking for a sample character, there should be a 5th level sample NPC in my guide for grenadier, although it doesn't include all the bells and whistles that make it amazing.
If your gm will let you be a small tiefling, you can trade their magic trait for a prehensile tail that can retrieve extracts as a swift, and their alternate favored class bonus is +1 bomb damage per 2 levels. Their racial stats are perfect for a grenadier +dex/int -cha. Plus you could be a literal wow imp hurling firebolts.