Custom anything in the firearms world implies budget--and it all depends on what's "custom" to you. Depending on what that is: If we're talking a total budget $1500, say--which is approximately 2x (or more) what you "need" (as a base condtion) for a quality, functional firearm (Springfield 1911, S&W M&P auto, Ruger Flattop .45 SA revo, S&W 686 .357 DA revo etc), I'd just look into a high end revolver--which doesn't mean all that "custom-built" at that price, but a decent quality firearm worthy of admiration. For a Single Action revolver that might mean Freedom Arms or an engraved or beadblasted and tuned Ruger, or just a stock US Firearms "Pre War" optioned out with Tru Ivory (faux) grips, or a nickel Colt SAA .45 with extra .45ACP cylinder and aftermarket stag grips.
In a Double Action revolver, maybe a Pro or Comp series Smith & Wesson with aftermarket Cocobolo (or whatever) grips. In an auto, perhaps a Dan Wesson Guardian or Valor (on sale)--both 1911 styles. Maybe a stainless and beadblasted Browning Hi-Power, flared ej port (etc)--which means some customization over a base $700 cost--with custom/Novak sights, etc.
$2500 budget for each of the above categories, maybe:
- engraved Colt Single Action
- engraved Double Action
- Ed Brown 1911 Special Forces or SF Carry (commander bobtail), Kobra or Executive Carry (Bobs) or Wilson Combat
...And it goes on from there.
Past the $2500-3000 point, arguably you're just spending money--especially as your first gun. Truly custom 1911s (the above might be considered semi-custom), can run you .$4-6k easily. Not recommended as your first gun, IMHO. Same for Single and Double Action revolvers.
Each of the above, depending on your taste, has a certain "june sequois" all its own in the appearance department, some adorned some not--just "classic/clean."
Some ideas.
Edit: some names in the single action world (esp Rugers but also some Colts): Bowen, Clements, Harton, Gallagher, Reeder.
1911 - a great number of them. Ted Yost is one I'm familiar with.
EDIT: since you (OP) say that appearance is important to you, maybe even paramount, a caution to a novice in particular, is that on an auto especially, most specifically 1911s, you can spend a great deal of "customizing" money without seeing visually significant "improvement." Reovlvers, generally at starting prices lower to begin with, can have major visual impacts by the time you're just starting mechanical customizing on, say, a 1911. For instance,you canhave a very "fancy, suctom tuned, stag or Tru Ivory (or even real ivory) gripped Ruger Flattop or Vaquero for the starting price on a high end Dan Wsdson Valor or Ed Brown 1911. Or an engraved and fancy wood-gripped Smith 686, etc, or a Sambar stag or real ivory gripped Colt SAA.