In the US, the rule is that once you assert your 5th Amendment rights, interrogation is supposed to stop: this does not even require you to have been arrested. If you have been arrested, then once you've lawyered up, you can look for an attorney. "If you cannot afford an attorney, one will be provided for you".
Phone rights depend on the state. In Nevada for instance, NRS 171.153 says
Any person arrested has the right to make a reasonable number of completed telephone calls from the police station or other place at
which the person is booked immediately after the person is booked and,
except where physically impossible, no later than 3 hours after the
arrest. Such telephone calls may be limited to local calls, except
that long distance calls may be made by the arrested person at his or
her own expense.
A reasonable number of calls must include one completed call to a friend or bail agent and one completed call to an attorney.
Ohio law even makes a useful suggestion:
such person shall be permitted forthwith facilities to communicate
with an attorney at law of his choice who is entitled to practice in
the courts of this state, or to communicate with any other person of
his choice for the purpose of obtaining counsel.
Cal.Pen 851.5 has a lot more to say about the call: within 3 hours, you get at least 3 completed calls, other stuff about custodial parents and additional calls; signs are required.
As far as I know, Washington does not have a statute guaranteeing a call, but you will be seen by a judge within 48 hours (probable cause hearing) so you will at least have access to a PD who can then communicate with the attorney of your choosing. (Policy may be that everybody does indeed get a call, there just isn't a specific statute). This article covers various case law findings that the right to a phone call is limited, and this gives a list (not necessarily complete) of state laws pertaining to the phone call.
There is no right to a phone book, and these days I suspect there isn't a phone book. Phone calls may cost money.