Had one built a year ago by Defensive Edge in Rathdrum Id. mine is only a semi custom as I used my Rem. LTR .223 as the donor.
Hart, Sendero taper, fluted, 1-9tw finished at 22in. $450
Chambering, fitting and install barrel $400
Square, true and lap $225
Cerakote everything black $225 (this is optional)
Reamer/go gauge from Dave Kiff $159 (also optional but I wanted to keep the reamer and go gauge)
Trigger on this rifle was the best factory trigger I've ever had. $0 (Jewel installed, usually $225-$250) Everything else I have has a Jewel. IMO, they are the best you can buy.
Dies will vary depending on who's you buy but you can probably figure around $200ish
Custom action $900 on up. Depending on who's receiver you purchase. Jerry Stiller makes and sells one of the least expensive and BAT is probably one of the most expensive. BAT, IMO, is one of, if not, the best action money can buy but I don't think a .223AI would know the difference between a Stiller, Defiance or BAT.
Selecting a stock and how much it will cost will largely depend on what type of stock you like and want. Don't forget there will be some added cost/s though. Depending on stock type, you could have the added cost of installing pillars, $200ish. At the least you'll have around $125ish for full action bedding. If you go with a wood stock there could be added cost/s to have it finished as well.
Like a lot of things, it's all about the details so ask LOTS of questions and do your research before you give anyone your hard earned money because all those little incidental costs can add up in a hurry.
Best of luck with your build!!!