What does a virtual person compete for?  Storage space, to be expanded as it grows through experience.  Also, existence. A hacker wouldn't just be a threat to an AI's financial situation, he could destroy or cripple the AI.  So security measures might be highly valued.  How would an AI protect itself from erasure?  By making a copy?  But then the copy, if it were exact, would be a competitor to the original.  So only an option if the AI believed its function was more important than its existence.  Or if it could be certain that no competition would exist between it and its copy.

And you didn't mention anything about the "person-ness" of the AI.  What rights does the original biological retain over the AI created from his/her personality?  What responsibilities?  Can the AI be a legally independent "person"?  Must it be?  If an AI must fight for its freedom, legal representation would be a financial need.  And then, once humanity realized that AIs can outperform them on so many levels they would start protesting and AIs would need to combat that with their own lawyers and advisors.  Anti-immigrant sentiment would give explosively away to anti-AI sentiment.  Saboteurs would spring up, requiring more expenditure to protect themselves (there's that hacker problem multiplied)

The AI would want external sensors and affectors.  Robot bodies, personal drones and satellites.  Electronically controlled vehicles to transport clients and friends.  Or would AIs even care what was going on in the non-electronic world?  Maybe some would and some wouldn't.

"Cloud" space is not just a virtual world where bits and bites float about without boundaries or limits.  The AIs would need to exist on physical hardware somewhere.  The casual duplication that people expect from the cloud wouldn't be a good option for a being for whom duplication has greater meaning than simple security of information.  However, any physical equipment is subject to failure.  Non-core information (information that is memory, as opposed to personality) could be replicated, but how would an AI protect its core personality against failure without duplication of self (assuming that wasn't what it wanted)?  What if it was "translated" into a non-electronic medium?  All programs can be translated to a series of 0's and 1's.  So what if it was able to translate its "self" into a series of sounds?  Or a machine that plays back a series of flashing lights?  Anything that could correspond to the pattern without having the function.  That might end up being really expensive.

Or maybe the AIs work out something where copies of the same AI are created and they regularly exchange checksums to make sure they haven't been corrupted.  Whole communities of like-sum AI beings routinely allowing other copies of itself to have the power to rewrite its core identity.  Imagine the chaos if something went wrong and two unlike AIs did a checksum...

As to what jobs an AI would be good at...anything involving repetition.  People get bored or tired and make mistakes.  AIs wouldn't.  For any jobs that require absolute precision, an AI might have a strong advantage.  Humans would still have the edge on true creativity, but it would be difficult to tell the difference between real creativity and what AIs do.  Take painting...once an AI learns how to paint, it could create exquisite paintings.  It could even teach itself to do abstracts.  Same thing for any art form.  The only way you could tell AI art from human is that human art wouldn't be as precise.

AIs could also do tasks that required isolation for long periods of time.  A human alone in space for decades might go crazy from the lack of interaction but an AI probably wouldn't.  Probably.

They could do any physical job that a robot could perform, and far better than a human operator of a robot could.