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

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.