Your bike is my age. I don't know how to feel about this.

You can do it cheaply, provided that existing parts (that don't need replacement) and the frame are compatible with modern parts. I think the Iguana frames up until the mid-90's were steel, so you may be in luck. Your goal, I imagine, is to make it functional. You don't have to get anything fancy. Get the 26-inch wheels that are made as replacement wheels for entry-level hybrids if they work. You'll probably need a new cassette and chain. Definitely new cables. If need be, there are relatively cheap shifters out there. If it's been sitting a while, new grease everywhere that needs it.

You don't need to replace the headset unless there is actually something wrong. I don't really care for the quill stem on mine, but I don't care enough to change it right now.