If you are seriously considering a custom website, you should keep in mind that almost every element of that design has to be hand crafted. When someone requests an assignment to be "custom", they expect the outcome to be unique. For instance, a custom logo design must be distinctive. However, it should be noted that word custom, when used as an adjective has a far different meaning than when it is used as a noun. As a noun it means a habitual practice; the usual way of acting in given circumstance. It also means a long-continued habit that is so established, that it has the force of law. Most dictionaries fail to adequately describe the definition of this word when it is used as an adjective. It's use has become "adaptive". When "custom" is used as a modifier it's meaning becomes quite the opposite. It goes from meaning conforming to meaning unique.
We are used to hearing the term custom built. When we hear that we assume that it is going to be different than something that is just built. A custom web design is a design that stands out from the crowd. It is designed to be different than its competition, more elaborate, more functional, more attractive.
In the world of website design, you would see the terms like custom web design, custom website design, custom web designer and custom website designer. In its plural form you might see custom web designs, custom website designs, custom website designers, You might even see the terms custom web page design or custom web page designer. As a plural you might see custom web page designs or custom web page designers.

I recently saw the phrase "build your own custom website" a feat that only a very few novices could perform. The skill level required to build a website that is truly "custom", is very high. It would require years of training in the world of graphic arts. That would mean a person would have to be a custom graphic artist long before he could become a custom website designer. It would also mean that a person would also have to be a custom website programmer and a custom web page creator. He would have to be a custom template designer which is a highly specialized skill.

The world of custom website design is a unique niche skill that comes from many years of experience and practice. Custom Website Development is a skill that should be left for professionals in this field.