How should I determine patentability and possible monetization of my work as a researcher?

Your question raises several issues.
1. Patentability
Patents are national rights, and the exact requirements for patentability vary from country to country, but at the very least the invention must be novel and non-obvious. You state that you have not seen any publication of similar work, which is encouraging. It would be a good idea to carry out an internet search of both journal publications and patent applications to see if any relevant publications exist. Patent databases can be searched for free, e.g. http://worldwide.espacenet.com/
Please bear in mind that your own publications (written or oral) may affect the patentability of your invention. In some countries such as the US there is a 12 months grace period in respect of the inventor's own disclosures, but in some other countries no grace periods exist in this regard.
A patent attorney can also advise you regarding the patentability of your invention, in particular as to whether your invention falls within one of the exclusions from patentability.
2. Ownership of the invention
I would suggest that you check with the university what their standard terms and conditions are regarding the ownership of intellectual property generated by PhD students. You indicate that you developed the method during your PhD, but that this research was not part of the work that the university had hired you to do. However, the assessment as to whether a particular invention forms part of someone's job or PhD duties is typically not straightforward and would have to e assessed by someone in possession of all of the relevant facts.
You should also clarify whether the PhD was funded by a party that might have rights to any of the IP, and whether any collaborators or colleagues were involved in the project.

Patentability for the US (I assume that your interests mainly will be directed to that country) consists of two aspects: 1) patent eligibility and 2) patentability in the narrow sens (i.e. novelty and non-obviousness). The second item has already been sufficiently addressed by Ms. Rigby.
For the US patent eligibility currently is in transit. At this moment the case law still would be dictating that business methods and diagnostic methods could possibly lack the extra technical character that would distinguish them from sheer mental processes or laws of nature. Thus, if your 'technical method' lies in internet applications for doing business or in methods to diagnose a disease on basis of the presence of biological markers, your invention could turn out to lack patent eligibility.

You've actually got several questions so here is a general guide

1) determine what is university IP and what is yours ... generally they have a policy handbook but the usual rule of thumb is if you use THEIR facilities or resources, they may have a claim. On the other hand, book royalties are not usually considered "university" so if pure software algorithm, you might have an escape (publish it and then after quit, work on applications).

2) talk to your technology transfer office (or there should be a friendly AUTM staffer around the city) to find how their views on commercialisation potential. If TT and you both agree that there is not much (obvious) value then just getting a release, especially if it is not time paid for under your stipend may be quick and easy. Public policy is that general jobs skills are not restricted whereas specific knowledge may be ... you might have to pay for sublicensing some uni IP as the counter-bargain.

3) determining the monetarisation is hard, a lot of lab-basedideas just don't scale ... if you spend say 1 man-year (amongst the generous spare time a grad student has :-)) then expect an order of magnitude resources to get to pilot scale and then more again for commercial launch. So even if the technique is novel, it;s incremental value may not justify the resources committed. This depends on your market and perception.

I suggest gathering data to make a business case, at least to justify in your own mind whether the idea is significant enough on its own or better to take the idea with you as your hiring credentials.