There is no such thing as a work visa. A visitor visa is 54 AUS$, a resident visa is 72 AUS$. Prices quoted are for singly entry visas.
Foreign nationals require a work permit to work in the R.O.C. Once you have a work permit, the National Immigration Agency (NIA) will issue an ARC (Alien Residence Certificate), that costs 1,000 N$ and is either paid by you or your employer. You cannot simply "buy" the privilege to live and work here.
Your employer procures a work permit for you. You need a separate work permit for each employment situation. There is no such thing as a work visa.
It is possible to attach a part-time work permit to your existing ARC. Note that any kind of work or non-essential activity requires a permit. That includes tutoring or volunteering. On this board there are documented cases of deportations for failure to have the relevant permits.
You need an employer who employs you for a minimum amount of hours and procures the work permit for you. Your ARC will be based on employment with this employer. You can addd additional part-time jobs. There is no such thing as a freelance ARC where you can have multiple clients/jobs. The minimum income is twice the basic income, somewhere around 49,000 NT$/month.
Very likely if you already have a job lined up and the employer fulfils the formal requirement to sponsor a work permit.