Whether you go with a big firm, a freelancer, or a church member, web designers can't do a whole lot for you without some important information. It's best if you know what you need to know before even meeting with someone about your new website. I currently have three websites on hold because clients simply don't know how to access some information that I need in order to work. That's frustrating for all parties, and it's often the result of poor practices by the old designer.
If you just want someone to take a look at the website and maybe update it a bit, you'll need the login information for the site. And it needs to have administrative access. I try to set up at least one person from the church with full admin rights, but it's not always a great idea to let every ministry leader have the ability to delete the whole site. I've worked with people who basically have an online business card, set up by some company that created some marketing information, and there's no login to be found. I've also worked with clients who only have limited access rights, meaning I can't really do a lot once I log in.
This is where your website is physically found, on a server somewhere, unless you host it yourself (unlikely). Your new web designer may want to copy files directly from the old host. This is especially important if there's a migration from an older version of a CMS (Joomla/Wordpress). But I know that most churches end up on shared hosting plans, so it makes sense that the old web designer may not want to allow the new designer access to it. Having admin backend login to the website itself is usually enough, but if you have the hosting login, that's good to have.
Domain Registration Information
Your domain name might be registered with your host, or it might be with a company that focuses more on domain names registration, like Google or GoDaddy. You'll need the login so that your web designer can assign your domain name to point to his/her hosting provider. Most website builders want to host on their own system rather than continue with yours. You also have to keep in mind that there's a yearly fee for registering a domain name, and if you want to keep the url, you'll have to pay it each year. However, you also have to avoid the scam emails that come in with people offering to renew it for you at a cost of $50 or something crazy. You should be paying $12 to $25 for this service, and Google even makes the registration anonymous for free (it's an expensive option on most sites).
If you need a domain name, it's best to keep it short. That's tough with so many taken, but you can try. Also, avoid anything other than .org or .com, at least until any of the others really make headway as legitimate domains. Anything that's .net looks cheap, and .church is rarely going to be second-nature.
Menu Items, etc.
Know the menu items you want to have on the website before you meet with the designer. You can always ask if there are some more ideas or changes, but trying to decide it all at the meeting is just a bad idea. You should also start trying to find photos for the website early in the process. Once a designer gets going, it's hard to change everything because you suddenly found the perfect photo for the home page. When you are redesigning a website, it's a perfect time to decide if it needs different menu headings or imagery, and that's all much easier to decide ahead of the designer starting to work.