It's unlikely that your wife will be able to live in HK.

I think the only way for an "ordinary" mainlander to live in HK is to have relatives already living there. Even then, they have to enter a lottery.

I have a friend in Shenzhen whose parents escaped to HK decades ago. They left her in China when she was a baby. She is eligible to enter the lottery, but she has no desire to do so.

Jobs in HK website:

http://hk.jobsdb.com/HK

There're more Jobs websites, if you Yahoo-gle 'jobs in HK'.

Best info about HK entry visas, you'll get at the Chinese Embassy. You could also ask for more info at your home Embassy in HK.

https://china.visahq.com/embassy/hong-kong/

Your wife will be allowed to come as your dependent,  but far as jobs go a word of advice, anything less than 25,000 HK dollars a month will make you live from pay check to pay check. Trust me, I've worked there and I'll never work there again due to the cost of living, I was making 30,000 HKD but wasn't able to save much. Here's a wake-up example:  Beijing apartment, 2 bedrooms: Y4500 to Y9000... Hong Kong (Chinese Yuan ) 2 Bedroom Y11,000 to Y20,000 RMB a month.... And those apartments are super small. So I hope you are a doctor, a tech or something more than a teacher, because you'll need to be to live with a family in HK. Good Luck! I mean that.

What jobs can a foreigner do in Hong Kong? Pretty much anything there is a demand for. You go to HK and you can see western people doing a much wider variety of stuff than you see in the mainland if only because there isn't the huge difference in salary expectations between a local and a westerner. 

That said, it's a fully mature job market so your prospects are going to really depend on where you are on the career food chain. If you aren't competitive for a certain job at home you aren't going to be competitive in Hong Kong either. There might be a shortage of accountants one year but a scruffy backpacker can't just show up and start reconciling some JVs. They can get good people there one way or another and can spot all the red flags in someone as well as any western market can. But if you are competitive for something serious you'll have a much easier time finding a job in HK than in the mainland.

I would imagine that you can take a pretty accomplished American consultant from PWC or EY and (if they are for some reason dead set on getting hired in China) stick them in a big city here handing out resumes and they really might have a tough time getting hired. Even if they're absolutely fantastic and have 10+ yrs of experience at a top firm they still might have trouble unless they get lucky or are willing to take a huge drop in compensation. Meanwhile that same guy could walk into any number business types in HK and garner a ton of realistic interest.

But then if you're a 23 year old humanities graduate or someone whose entire resume is retail service in the west and ESL in the east and your goal is to just make a halfway decent living you'll have a much harder time in Hong Kong than mainland. Im sure they have kindergartens in HK that hire westerners but you'll be paid the same salary (relative to everyone else in the society) that somebody working at a kindergarten in the US makes. So there's not going to be that "expectations gap" where you'll feel like you're doing good cause most everyone else is poor and rents are cheap. You will feel thoroughly working-class doing basic ESL in Hong Kong. Either that's something that person can live with in order to get out of mainland china or it's not. 

Like ironman510 said, you can be making $50-60K USD/yr in HK and feel like a total bum. It's not like here where that level of income (within reason of course) gives a ton of control over your life. 

I absolutely LOVE Hong Kong and if I stay in Asia that's where I would want to be, but I'm still not senior enough to make living there a no-brainer based on the jobs I could realistically compete for (either in finance or consulting).

For me HK the magic number is about $100K USD/yr... and ideally more. That's where I feel like i'd be making enough to enjoy the benefits of the place while offsetting the drawbacks. Much less than that you're either living in a closet, sharing an apartment with someone you aren't sleeping with (which is a total dealbreaker for me), living paycheck to paycheck or really just not ever leaving your apartment or eating out. And then what's the point? Why live in a place with stuff to do if you can't afford to do it?