Not having an Apple IIc handy but wanting the experience I went to http://www.calormen.com/Applesoft/index.htm and tried out the Applesoft Basic simulator that runs in Javascript. As others had said, no pre dimensioning/declaration of string variables necessary. Unless I am operating this simulator incorrectly, you can input statements including strings to be compared in mixed upper lower case, but the keyboard input received in input statements is upshifted to all caps. So your tests of any sting loaded from an input statement should read if a$ = "STRINGINALLCAPS" otherwise the comparison fails. You can still PRINT "UPPERlowercase" and that displays both cases. Acts like my keyboard is stuck on caps for input statements only.
10 home
20 input "What state do you live in?";a$
30 if a$="OHIO" then goto 50
40 goto 10
50 input "Correct! Type 'next' for the next question.";b$
60 if b$="NEXT" then goto 70
62 home
63 input "Type 'next' for the next question.";b$
65 goto 60
70 home
80 input "What month is this?";c$
90 if c$="FEBRUARY" then goto 110
100 goto 70
110 print "Correct! Thus concludes this program."
115 stop
120 end
10 home
20 input "What state do you live in?";a$
30 if a$="OHIO" then goto 50
40 goto 10
50 input "Correct! Type 'next' for the next question.";b$
60 if b$="NEXT" then goto 70
62 home
63 input "Type 'next' for the next question.";b$
65 goto 60
70 home
80 input "What month is this?";c$
90 if c$="FEBRUARY" then goto 110
100 goto 70
110 print "Correct! Thus concludes this program."
115 stop
120 end