Is the following sentence grammatical?
To proceed setting up your account, click here.
I'm suspicious of the word proceed in this context — isn't the word continue a much better fit?
I agree. "Proceed" needs a preposition like "with", "against", or "to". "Continue" can be used with a preposition but does not require one.
In your case, there are probably some initial steps to be taken before setting up a web site such as "paying money" or "filling a form of personal information" e.t.c. So, setting up a web site is another new step after those steps.
If so, I would use proceed to.
proceed to: to do something after doing something else; to do sth next, after having done sth else first.
Also, proceed to and proceed with may slightly differ in meaning / sense
proceed with: to continue to do something that has already been planned or started
In your case, using continue might also be possible. But you should be careful with the context. The closest senses of continue:
1) to keep existing or happening without stopping
2) to start again, or start doing something again, after an interruption