I wouldn't bother with Kosci, there's a lot more interesting spots. As previously mentioned, it's best to park in the overnight car park at Guthega. Keep a shovel in the car just in case you have to dig yourself out. Access to the main range via Illawong can be very difficult due to poor snow cover at times. I also find it a bit of a boring way in. It's quicker to head straight across the dam and follow the valley up via Tate East ridge. Take great care in the first little section past the dam, if it's icy. I've written several letters to P&W to extend the 4WD track but alll I've had is "we'll look into it". When the valley flattens out, you have the best camping you'll find anywhere, with lots of shelter and running water. It also has the easiest, fastest and safest retreat if bad weather hits.
A GPS is absolutely essential (and hope they don't spend a day reprogramming the satellites as happened to me on one trip). Try following a compass bearing in a whiteout for a day to discover why. From your camp you can almost always guarantee good snow to play around in either on the Tate East ridge side, the Guthega trig side or at the end of the valley. Keep heading up to the fantastic panorama at the top of the main range. I'd also recommend a PLB.
For a beginner, spring is the best time to go. Ego snow. Nothing like the spring slush in the resorts.
I've always preferred lightweight gear. 'An ounce on your feet is equivalent to a pound on your back.' Good technique will allow you to parallel and tele almost anywhere. I've found that heavy gear will allow you to do amazingly tight teles with one hand dragging in the snow but I feel the extra weight isn't worth it. Inflexible bindings make touring a chore. My preferred boot was the Alpina 2000 (I bought my last pair new from US, on ebay for $20 after they had stopped manufacturing them for a period). Here's me in the area I mentioned on lightweight gear with my vintage tonkin cane poles: http://www.youtube.com/watch?v=2mkLLdtzZzc I learned to tele back in the days when teles had been forgotten, from the book "the Wonders of Skiing". There are 3 styles of tele, with mine being the trad style.
One final note on snow caves. They take a long time to build and despite the best intentions and design, can be lethal. Don't forget the 4 young fellows from the Rockhouse who perished in one some years back.