It's going to be a lot like owning a Cobalt.
2.2 is great overall. Super easy oil change, probably the easiest ever. The air filter is a little bit of a pain though if I remember right.
Interior door handles break like crazy, but are still readily available from GM as a handle kit. The throttle body and pedal position sensor can go bad, but neither is a super-major-bad issue.
EPS can have problems. I believe these are part of one of the EPS recalls. They are part of the ignition switch recall.
A well kept HHR is fine, a lot of people just tore them up because they were a cheap crossover kind of thing and ended up on buy here pay here lots frequently.
eljefino has one and doesn't post many projects related to it, so I assume it's reliable for him.