You have spent your life in your house for the research of potions, testing experiments or making some metals into gold, so that you could have more gold peices. A rare background, not many have experimented with metals and maybe even dangerous ingredients, not many have the equipment that you have, they are too expensive and most can't spend money on something like that. 

Choose a potion or some magical substance that you have from your background, and work with your DM to see what that might be. The equipment section in the PHB contains some cool items that could be the potions or magical substances which you possess. Or you could make something totally new, but make sure your DM knows what you are doing.

Skill Proficiencies: Choose two skills from Animal Handling, Arcana, Deception, History, Medicine, Nature, Perception and Persuasion

Tool Proficiencies: Alchemist's supplies, brewer's supplies, poisoner's kit,

Languages: Since you need to understand all books of science and alchemy that have different languages, you get three languages of your choice

Equipment: A diary that you wrote in full of entries of possible scientific breakthroughs, a bottle of ink, an ink quill, an acid vial, an antitoxin vial, a flask of holy water, an hourglass, a hooded lantern, a magnifying glass, a steel mirror, a basic poison vial, 17 empty vials, an empty flask, a merchant's scale, a set of common clothes and a pouch containing 20 gp

Suggested Characteristics

Alchemists are shaped by their experience in alone, obsessing over or science, potions and wealth. The only time they see other people are when they are advertising their product in the market/merchant part of the village or city. Their goal in life is to be wealthy, immortal and super strong. They're so dedicated to science that some could forget about their goals and put science ahead of their life.

d8	Personality Trait
1	I idolize a great alchemist, and constantly refer to that person’s experiments and finished pieces.
2	I won't fight someone if they're too powerful or strong, which is almost everybody in my opinion, all of my finished pieces are for other people to use, unless it's a special one.
3	I see affects and effects in every event in an experiment. The science is teaching us, so we must understand it.
4	Nothing can shake my lonely and brainy attitude.
5	I quote great alchemists in almost every situation.
6	I am tolerant (or intolerant) of other alchemists and respect (or condemn) the experiments of other pieces.
7	I’ve enjoyed rations, experiments and loneliness in my room for alchemy, though I would like my life to be more luxurious.
8	I’ve spent so long in my room of alchemy that I have little practical experience dealing with people in the outside world.

d6	Ideal
1	Tradition. The ancient traditions of alchemy and it's method must be preserved and upheld. (Lawful)
2	Knowledge. I always try to help the knowledge and understanding of alchemy, no matter what the personal cost. (Neutral)
3	Change. We must help bring a better and different understanding of what science is trying to tell us. (Chaotic)
4	Power. I hope to one day rise to the top of the greatest alchemists. (Lawful)
5	Faith. I trust that science will guide my actions. I have faith that if I work hard, things will go well. (Lawful)
6	Aspiration. I seek to make a difference in the understanding of science and alchemy by contrasting my actions against my scholar's teachings. (Any)

d6	Bond
1	I would die (or try) to recover an ancient finished piece of alchemy that was lost long ago.
2	I will someday get revenge on the evil alchemists that labeled me in public as a unworthy alchemist.
3	I owe my life to the alchemist scholar who took me in when my parents died.
4	Most things I do is for the common people.
5	I will do anything to protect the school where I learned the basics of alchemy.
6	I seek to preserve a sacred alchemist's diary with entries of science breakthroughs that my enemies consider worthless and seek to destroy.

d6	Flaw
1	I judge others harshly, and myself even more severely.
2	I put too much trust in the merchants that sell my goods, I'm not a buisness person, they could be taking more money than what we agreed on.
3	My curiosity and obsession of science and alchemy makes me blindly walk into dangerous and illegalfinished pieces.
4	I am inflexible in my curiosity.
5	I am suspicious of strangers and expect the worst of them.
6	I become obsessed with my goal to the detriment of everything else in my life.