For independent study a leaner approach might be best (the open logic textbook is meant to be remixed to form a course, so it includes a lot of material). I think Daniel Velleman's "How to Prove It" is a good textbook for learning to deal with proofs, plenty of exercises there and it has a more practical approach (it is intended for CS and math students). Volker Halbach's "The Logic Manual" is good, as is Restall's "Logic", although both are oriented to philosophy students.

EDIT: s/"How to Solve It"/"How to Prove It".