Creating a non combat charecter more alchemist mage and it will be a Breton any advice

For the easiest option, take the Mage birthsign, for a much more interesting option take Atronach, you are nearly immune to magic but will need to make plenty of restore magicka potions.
Nothing wrong with taking a combat major skill you will never use ( blunt for me ), acts as a level cap.
If you want non combat, illusion is your best friend, buy all the spells you can, then use those altars to make your own versions.
It is kind of traditional to take Mercantile with an alchemist, but you might not like the lack of control over levelling.
If you don't want to use destruction, remember absorb health can save your skin if combat becomes unavoidable.

For an aggressive playstyle, the Apprentice birthsign will serve you well, though you'll have problems agains necromancers/other spellcasters in the Mages Guild questline.

The Mage is probably the best choice if you're not going to be a combat mage. Not much more to say. Not anything I can think of.

You might want to clarify what you mean by non combat. Will your alchemist use a weapon to help apply poisons? If interested in avoiding the classic fire/ice/lightning spells, illusion + conjuration is very effective, especially when backed up by restoration for buffs and absorb health. I'm talking capabilities here, not major skills. I pick majors only to control leveling. I think the mage birthsign would be good here; with a Breton it is nice, simple and quite defensive. Good luck.

If you mean combat-avoiding, then the two skills you need to build up are Conjuration - to summon a creature to do the combat - and Illusion - to persuade an enemy to do the combat. Since both involve casting spells you'll need to be able to dispel Silence when it's cast on you, and that will take a potion, since you won't be able to cast. That requires alchemy at a sufficient level, or a lot of luck finding the right potions!