I intend to create a website that acts as a business card for someone, as a present.
Websites such as www.about.me seem suitable for this purpose, however, the cost of obtaining a domain is unreasonably high, and I prefer to host the website on my server at a lower cost.

Are there any pre-designed layout options available for such sites? A single page with links to social media, email, and an attractive layout is sufficient, without any additional features such as a blog or photo album.

Purchase a hosting plan for $5 per year that does not include MySQL or other additional features, add your domain to it, and create your HTML page.
This is the most affordable option available.

In my opinion, it is possible to quickly find someone who would offer a template on webmaster forums such as http://www.seomastering.com/seo-forum/index.php and even provide it with content for a small fee.

It's possible to bootstrap and regarding the expenses - it's simple as the domain .com costs only $10 a year, and for hosting, you can opt for a basic one without requiring PCP or muscle for support.

Indeed, there are several pre-designed layout options available for creating a simple business card website. You can look for "one-page website templates" or "personal portfolio templates" to find designs that match your needs.

Many websites offer free or low-cost templates that can be easily customized to include links to social media, email, and an attractive layout. You can also consider using website builders like Wix, Squarespace, or WordPress, which offer a variety of pre-designed templates that can be tailored to your requirements.

Additionally, to keep costs low, you can consider using a subdomain on a free hosting service, such as GitHub Pages, or finding affordable domain registration services to purchase a domain at a reasonable price. With these options, you can create a personalized business card website without breaking the bank.

If you're looking for some specific platforms where you can find pre-designed layout options for your business card website, here are a few ideas:

1. WordPress Themes: You can explore the "one-page" or "portfolio" themes available on platforms like ThemeForest, Elegant Themes, or the WordPress theme repository. These themes often come with customizable options for adding social media links and email contact forms.

2. HTML/CSS Templates: Websites like HTML5UP offer a collection of free, responsive HTML/CSS templates that are perfect for creating a simple one-page website. These templates are easy to customize and often include sections for showcasing personal information and contact details.

3. Bootstrap Templates: If you're comfortable with working with Bootstrap, you can find a variety of free and paid templates on websites like WrapBootstrap or Start Bootstrap. These templates are mobile-friendly and can be easily adapted for your business card website needs.