I've come up with something along the lines of this so far:
1) Split the 100ml beaker contents into 2 separate 50ml beakers.
2) In the first beaker, add NaC2H3O2 to precipitate silver.
3) Then Add in NaOH and see if it dissolves. If it does dissolve, we know there is Ba present. If it doesn't, we know Ba isn't present.
4) If it isn't present, we add in Na2SO4 to precipitate Pb (as Na2SO4 precipitates both Pb and Ba).
5) Finally, we add in NaCl to precipitate Cu if Ba isn't present.
Now in the second beaker, used only if Ba is present, I would still add in NaC2H3O2 to precipitate silver, but when I get to adding in Na2SO4 (knowing that Ba is present but not knowing if Pb is), I'm not sure how I can prove whether Pb is present or not. What could I possibly do?
Also in the table we were given, C2H3O2 1- is soluble with everything but Ag.
Edit* I noticed that in the table we were given, Cl- and other halides have Ag1+ and Cu1+ listed as exceptions, but the question asked us to find out if Cu2+ is present or not. In this case, would adding in NaCl to a solution possibly containing Cu2+ cause a precipitate to form? Even if the charge is different?