If you are flexible in your dates, mid Feb gives the best chance at great snowboarding conditions. Park City resorts are at lower elevations than some other well known destinations. If UT has a bad snow year like last year, there won't be a ton of natural snow until after the Jan storms. Don't get me wrong, there will be snow either way. Even if there is low snowfall, the resorts in Park City make a lot of snow with machines. But if you are coming all the way from Sydney, I'm guessing that you are wanting more of the Utah "greatest snow on earth" experience. That experience is a combination of a solid deep snowpack underneath many layers of progressively lighter and drier powder, but the powder can't be too light. It still needs enough "body" to support the weight of the rider, otherwise the board cuts all the way down to the icy pack underneath, or you find yourself so deep in it that you have to struggle to stay on top. Good snow (which UT claims to have the best of) is not so wet that it gets sloppy and crusty, but not so dry that you have to fight to stay on top of it when the powder gets DEEP. It should have a sort of "bottomless" feel that you can just float on top of with minimal effort.
If you come in early Jan, you risk conditions that have a lot of icy spots from man-made snow that is very poor quality compared to natural powder, and if Dec. isn't particularly good, you end up with some thin layers of powder on top of a crusty mess underneath. Not what you would travel around the world to ride on. Late Jan is starting to get really good, but if you are trying to avoid holidays, you absolutely don't want to be in Park City during Sundance Film Festival. From the week before Christmas to the end of Jan is the busiest time of year for Park City.
Feb is my absolute favorite ski month though. By then, there is a very deep solid snowpack which prevents you from bogging down and having to work much harder, but there are about 11 precipitation days in a typical February, so mother nature is laying down fresh powder every 2-3 days. Also, temps in mid Feb are getting warmer and there is much more sun than Dec-Jan, but not enough to cause sloppy snow.
Re: accommodations, there are less expensive places in PC for sure, but remember that it is high season for them. If you don't feel the need to stay directly in Park City, consider staying in SLC and just renting a car or catching the shuttle to whatever resort you want each day. More bang for your buck that way. You would also have the option of going to some of the other SLC resorts. When I snowboard, I particularly like Snowbird and Brighton. But they aren't nearly as large as Canyons in Park City.