If you’re going to get your webspace built by someone else, you need to find a company or individual that listens to you, understands your needs and is open and honest.
You also need to have good vibes and trust your instincts about them. They will produce a far better product if you’ve been able to communicate happily during the project.
Have a good look at their website. Do you like it? Is it easy to use? Are there any typos? How’s their grammar? If you like it, there's a good possibility that you'll like what they design for you... and vice versa.
Here are some questions you might want to ask:
How much do they charge and what does that cover? What costs are one-off and which might be ongoing?
Are you tied into a contract with them? What will be the situation for your webspace if you decide to move to a different web design company?
What will be the situation with your webspace if their company folds?
Does the cost include the registration of a domain name? Will the domain be registered to you?
Which company will your domain be registered with, where is it hosted and for how long?
Can your webspace be easily viewed on a tablet and mobile?
Are they using templates to build your website or designing it themselves from scratch? Which package are they using to build your website?
Are they building a website you can edit yourself or will you need to pay them to make changes? If you can make changes yourself, is that for the whole website or just parts of it?
What support can you expect, for how long and at what cost?
What’s the timeframe for completing the work? Does that fit in with your needs?
Will they keep you informed of ongoing progress, so that you can comment on what they’ve produced so far, or will they just present you with a finished product?