When it comes to building a custom rifle, there's alot to "unpack" there. I would take a good look around for a "turn key" factory rifle first? lots of calibre offerings from Tikka, and as a "lefty" they have several models. Failing that, you can get a smith to chamber up a barrel and action, stock options these days are many, Manners offers a "mini chassis" which is a good alternative to bedding. Spend the money on the best barrel you can afford.
If you can source the parts yourself? like the stock and barrel, that may save you some time and money?
Good Luck, Cheers