I'm at a disadvantage in trying to choose a tray format for you as I have no idea what slide tray formats are/were common in Australia.
My first question would be "How many slides do you have". If the number is fewer than about 500, a well designed manual projector may be the sensible answer. If you have a few thousand to see, the faster operation of a slide projector using a tray would be worth it.
That being said, the European Straight tray is quite rare in the USA, and I do not have a projector using it at present. The popular trays in the US were the Airequipt metal magazine and TDC/Universal (plastic) tray (mid-1950s-early-60s) followed by the Kodak Carousel and the Sawyer's Rototray (mid-1960s-circa 2000). I would avoid the Airequipt-using models for two reasons: 1) since each slide goes into an metal frame, which in turn is inserted into the metal magazine, it's a royal pain to use them unless you intend to keep the slides stored in the trays and 2) it seems the the friction of those metal frames against the walls of the magazine increases with age, causing jams.
The Carousel trays are extremely unlikely to jam, but the truth is that the Sawyer's Rototray is just as reliable so long as the slides are intact. The Rototray-using models are mechanically simpler than the Carousels, and easier to repair if something goes wrong with the projector itself. Most projectors that take the Rototray can also used slides in TDC/Universal straight trays (Carousels can use only trays made just for Carousel. Carousel projectors can also project slides manually - insert a slide into the slide gate upside down, and press SELECT to make the slide pop out like a piece of toast!)
Two other notes - not all Kodak projectors are Carousels. Kodak make manual projectors early on, than had ones using the Airequipt Magazine or a built-in stackloader, followed by their own straight plastic tray format called Cavalcade, before rolling out (no pun intended) the Carousel in late 1961.
There were projectors sold under the Hanimex brand sold in the US in the 1970's and 1980's that used the Sawyer's Rototray. I don't know whether the Hanimex Projectors sold elsewhere used the Rototray or not (The Rototray stands up inside the projector like a Ferris wheel, now flat like a Carousel)
Things to consider when buying a slide projector would be to make sure everything is there, make sure the power cord is in perfect shape, that everything runs, and check the availability and cost of bulbs on the open market (i.e., find the code for the bulb the projector uses and check internet auction sites for that lamp code).