Zucchini and curcurbits in general are usually no problem if the fruit is off the ground, so trellising sounds like a good idea. Heavy fruit like pumpkins can't be trellised and take up a shittonne of room, so might not be the best use of space. If you do have a try at pumpkins you might need to put a tile or plank put under each fruit to keep it off the ground.

Root veg would be better in pots or similar. As I didn't have room or good soil for spuds in East Brunswick, I grew spuds in car tyres stacked up on a concrete base. Made harvesting easy too as all I had to do was pull each tyre off in turn and fumble out the spuds. Very very productive way to grow spuds. Round carrots & beetroot went in milk crates lined with shademesh - these worked very well and also worked for leeks and silverbeet. I am too cheap to buy large pots from the green store. I found 1 bag of potting mix fitted nicely in 1 milkcrate too which made planning easier. Milk crate gardens did need extra watering in summer as they did dry out a lot if I didn't watch them. One benefit was they were easy to move about in accordance with the weather/sunlight. I've tried using growbags, but I find them a bit heavy to move about. They do hold a lot of soil so could be good for big carrots etc that need a deep soil bed without lumps in it.