It’s what’s underneath that counts…
The starting point for many firms in acquiring a new website is to look at a number of agency websites folios to review their work and who they have worked for.
That’s fine but any competent agency with longevity in the field should be able to build you a nice looking website that works.
Next step would be to put together an RFP to a number of agencies that look or sound good on the surface.
I don’t blame you for taking this approach because most agencies struggle to differentiate themselves beyond what they look like which should be exactly what you DON’T want for yourself.
Good design is important (and it’s not that hard anymore) but what really matters is not what’s on the surface or your opinion of what constitutes good web design, what really matters is the bits you can’t see and probably never will unless you are the target audience.
The right agency for you should be obvious and ideally they found you before you went looking.