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The invitation letter, work visa and resident's permit. Normally he also is responsible for your medical examination IN THE MAINLAND (but not in the country of your origin).

This is in t h e o r y , of course, not always reflecting reality. Your case seems to be one of those borderline situations!

You should first make sure your employer has the legal wherewithals to sponsor you as an employee; he must have a licence with a number to hire foreign nationals.
If he doesn't have such a licence you had better refrain from getting hired by him.

Now as for the practical side to your problem: Getting everything paid by your employer may hinge on your negotiation skills. Your employer has the longer arm than you.
Would you still care for that job if you had to fork out the money to pay for a round trip to HK and purchase the visa there? Is the job so good?

As for the actual costs of such an undertaking: your accommodation costs in HK need not exceed 100 kuai a day. You can stay at the Youth Hostel on Mt. Davis, WesternDistrict HK Island, ca. half an hour from Wanchai. In Wanchai is the China Visa Office, 26 Harbour Rd. I think they take a working day to issue you with such a visa, maybe two days but not longer.
Don't bother buying a visa through a travel agent since the visas agents can procure do not include the work visa. You will pay about double for an 'F' visa but that 'F' visa will be for the purpose of making business trips to the Mainland, not for "cultural activities" (the second reason why 'F' visas are issued).

Your biggest budget item will therefore be the visa cost itself (probably the same as back home) followed - or preceded, as the case may be - by the outlays for transportation to and from your current whereabouts.

Again, this is supposing you really want to get that job, and your job is legal and legitimate... Maybe you stand to get an extra bonus for good behaviour?