How to go abouts the ins and outs of work visa applications for Australia

Hello everybody

I am trying to figure out what are my best options for a successful work visa application for Australia.

I am 36 yrs old and just recently completed my high school teacher certificate from the University of Victoria's Post Degree Professional Program with my teachables being Spanish and French. From what I understand, I am not eligible for the Working Holiday Visa as I am over 30. I have applied to the Education and Training Department for New South Wales where they told me that everything is in order except for the fact that they do not offer work visa sponsorships. I have since figured out that the next possibility for me would be to apply for the Skilled Migration Visa. From what I have read, I seem to be an ideal candidate because secondary teachers are on the critical demand list. Unfortunately, I do not have the necessary 12 months teaching experience from the past 4 yrs seeing that I just recently graduated. I have my practicum experience from this past January to the end of April. I also have 2 yrs experience teaching ESL in Taiwan but unfortunately I don't have the necessary paperwork that OZ immigration would want.

Is it possible to go to Australia on an eVisa (tourist visa), look for work, get the necessary work visa sponsorship from the said school and start working or is that the hardest option?

Is it also possible to apply for a Skilled Migration Visa, go to Australia on a tourist visa and and hopefully get the skilled migration visa approved while in the country?

If anybody out there has any information or advice whatsoever that might be beneficial to my situation, that would be greatly appreciated!

Cheers and I look forward to reading some of your replies!

Dave