When non-profit organizations are young and bootstrapping, they generally don't have any budget to pay for a professional website. Fortunately there's almost always a volunteer around who will take on the job of making your organization a site.
We work with a lot of non-profits who are making the big leap from "free volunteer-maintained website" to "cold hard cash money website". It's rarely as smooth a transition as we'd like, and a lot of that grief comes from the way the free sites were set up. Some tips to save heartache:
Register your own domain.
Transferring domain registrations is a hassle at the best of times, so start right and make sure that your organization (which uses the domain) actually owns the domain. Having it registered by a well-meaning volunteer in their own name might seem simpler right now, but trust me on this one. If someone wants to cover the cost of the registration, that's brilliant. Have them donate $20 to your org to cover the costs rather than paying for it themselves.
Use email addresses @yournewdomain.com.
If you are running PaisleysForPeace.org, use firstname.lastname@example.org, not email@example.com. You just bought a domain! Use it.
If I was feeling snippy, I would say "Because no one should ever give money to someone using a free @yahoo address". The more salient business point is that using an address at your own domain builds brand recognition, is more professional, and is just plain easier for people to remember. Even if your organization is 2 people working on a card table in your dining room, you can set up info@, marketing@, donations@ and so on. Mail sent to those addresses may all end up in the same inbox, but when you're small it can help make your org seem big, and when you're big it will help keep you organized.
Your site needs to be built in a Content Management System (CMS).
A CMS will allow you (or someone else in your organization, including your plucky volunteer) to easily change the content of your site. You don't need to know how to program or how to read code. The skill level you'll need is right around "can write a letter in a word processor", which is great because, hello, you have no free time. You are busy trying to save the world!
The first years of your organization are probably when it will undergo the most change. At the simplest level, a service that you currently offer only to "cats and dogs" may soon expand to "cats, dogs, small rodentia, and ferrets". You may outgrow your dining room and move into your own office, or a shared non-profit space. You may grow or adjust your mission radically, and you should be able to update your site to reflect the changes.
The CMS should be popular.
Some of the simplest and most popular are Wordpress, Tumblr, and Blogger*. Insist that your volunteer use one of these services (or another that you're comfortable with). Your intrepid volunteer may be a student or otherwise eager to use this project to explore a new system, or maybe they want to build the site from scratch to teach themselves how to do it. Whee! We're all for learning! But not at the expense of your website. Be firm.
* "But this is a website, not a blog!" you might point out. That's OK. A blog is just an organizational structure, and your volunteer should be perfectly capable of using the CMS to make informational pages instead of a blog.
Popular services mean tons of support available (sometimes from the company itself, or from other users), and lots of people who are familiar with using the service. If your volunteer moves away or gets poisoned by a platypus spur, who's going to make changes to your site? It's like buying a Ford instead of a Lada -- there are lots of mechanics around who know their way around a Ford. What's a Lada, you ask? Exactly.
Your site should hosted by a 3rd party, not the volunteer.
Do not under any circumstances allow the hosting of your site to be on anyone's private server. Do not let your volunteer "just tuck the hosting in under their own account" in order to save money.
Whoever controls the hosting controls your site. They're like your site's landlord, and you want to be your own landlord. If you're using Tumblr or Blogger or Wordpress.com, you're golden because hosting is part of the whole package with those accounts. If you are using a Wordpress installation [WP can be run on WP servers, or off your own server] or some other CMS, insist on controlling and paying for the hosting yourself. It doesn't have to be expensive, and having complete control over your site is worth the expense.
It is worth the small amount of extra work and money to make sure that you have full control of your domain and site. Hopefully this advice will help you and your organization build a solid first website and put you in a good position for an upgrade when the time comes.