For general adventuring and exploration, an alchemist has a lot to offer as a utility character. He is always ready to hand out healing potions, antidotes and other remedies, and willing to brew more. He can identify recently discovered potions. He can find useful plants, minerals, and other components while foraging in almost any environment.
A more challenging question for creating the class is: “What does the alchemist have to offer during combat?” One of the most common answers to this question is, of course, fire bombs, smoke bombs, TNT, and other variations on exploding projectiles.
My experience as a wizard (out of character for me, I know, but it was a very rewarding character to play) in a Fourth edition game led me to consider a slightly different answer. If the alchemist bomb is just a backyard science version of a fireball spell, then why not explore other spells for possible alchemy recipes? My wizard did more than cast magic missile and fireball spells during combat. He was a controller, adding area affects to control enemy movement, using magic to boost combat effectiveness of allies while decreasing the same in our enemies. So, I decided to design my alchemist class as a controller.
Some spells that could be modified and repurposed for area effects include Fog Cloud (reduce visibility), Stinking Cloud (induce nausea), and Web (for a sticky floor – difficult terrain). One potion that comes to mind for boosting your allies in combat is Shot of Courage (temporary hit points). Recipes for causing distress to individual enemies in combat include Itching Powder (causes discomfort – disadvantage to attacks), Flash-Bang (blind and deafen enemies – surprise round), and Blinding Dust. These could give the alchemist some versatility during combat and help the character have something meaningful to add.
It probably wouldn’t hurt if he also knew how to use a dagger.