Depending on how much luggage you have with you, you might want to take the bus (810) from Memmingen airport to the Memmingen Bahnhof. There are luggage lockers (Schließfächer) at the Bahnhof where you could store your luggage. Then you could do the rest of your business` hands free. The bus leaves the airport at 10:10, 11:33, and 12:00 and takes 10-12 minutes to the Bahnhof.
According to Google, the C&A store is a ½ km (about 6 min) walk from the Bahnhof.
Here is information about the Bahnhof and the surrounding area. It looks like there is not a restaurant in the Bahnhof, only a bakery, but there are several restaurants across the street and some in Schrannenplatz, by the C&A store.
Forget what I said above about bus times. That was for work days (M-F). I guess you are arriving on a Saturday; the schedule for 2015 is here. Look at the schedule under "Samstag (Saturday), Allgäu Airport - Memmingen ZOB". There is a #2 bus at 9:27 (in case you arrive early). At 10:40 there is an AST (Scheduled Call 'n Ride Shuttle), and at 11:02 there is a #811 bus. The fare for any of these is 3€ for 15 and over, 2,25€ for 4-14.
If you are going to take the AST, you have to arrange it in advance, at least 60 minutes. If you call from outside Germany, you call the country code for Germany (49) then 1802 908070. If you call from Germany but from a different "extension" than 1802, you call 0 1802 908070.