For me, a full custom rifle has always meant pure American Classic styling: A straight no comb stock with very little drop if any at all; a very open pistol grip; French Walnut; 22+ LPI intircate checkering, appropriate metal checkering and modest engraving on case hardened receivers.
A Pre-64 Win action or a good Mauser action fully worked over by a good metal smith for a bolt rifle is a must..
This is an example from The Dave Miller Company in Tuscon, AZ. The pic is kinda' small but you can see the general trend. Dave Miller (metal smith) and Curt Crum (stock maker) have together built some of the finest custom rifles around.
A couple of other examples from Stephen Billeb's web site: I'm not sure he did all of the work on these as many custom rifles when being built are "farmed out" for special work done by others than the primary builder such as special engraving,etc.
Here's a link to Stephen Billeb's web site: He lives in Cody, Wyoming and is a well know custom gun builder with an international reputation. There are others ....
http://www.customgunmaker.com/
You might check this web site for a list of very good rifle builders. Anyone here will be pricey to the extreme, but the work will be beyond belief. Not all of the best US gun makers are members, but anyone who is listed is capable of building a work of art.
http://www.acgg.org/
If you're building on a Ruger #1, a very functional custom feature is to get rid of the long safety and have a new safety button built from scratch that is shorter and not in the way.
-BCB