For your first trips out, I'd recommend staying with the pack. Mostly for safety sake, but also to learn what the more experienced there are doing. If you don't have a map of the chain, I'd get one. The most important reason being that the chain is a system linked by the Fox river and ice can be great all over the lakes, but dangerous wherever the river current runs. I've fished many years on the chain and the one time I found myself really scared and thought I might be going in was when i wandered into the channel area off of Marie and decided to head back onto the lake ice over a pressure ridge that was not the way I originally went.
On the brighter side, a map will also show you the obvious things like depth contours, access points, structure etc. Get the maps, pick out a few spots you think should be good, head up there and if there is already a group or a few people on that spot, it's probably got some fish on it. Just be courteous and non intrusive and you'll find most people will be willing to help you out once you're on the ice.
Here's a starting point for you. Try Pistakee first. Park at the Oak Park Lounge (pay to park inside, I think it's $5 still 801 Oak Grove Rd, Johnsburg, Illinois 60051). The shoreline runs at an angle to the southwest there. Follow the shoreline until you line until you are straight our from a house with a green roof. Fish in the 16 FOW range and work various depths there to see what works. If that doesn't pan out, head straight south across the bay towards the point. Fish the deeper areas in the 20 FOW range and see if you can find some fish there. If all else fails, continue southwest towards the road bridge and fish the 6-10 FOW areas of the bay which almost always produces bluegills (not big ones usually, but at least something that bites).
Hope that helps your intro to the chain. Oh, and if you hear a group of rather loud, Romanian/Russian accented (alcohol breathed) guys fishing that area, keep your distance (they're all crazy...LOL) but watch what they do, they are good sticks that know that lake like the back of their hand and do very well there. If you're brave enough, offer them some Vodka and ask how they are doing (ask for Lance if you do). Good guys, all of them, just a bit crazy...
