Hi NoChaos. Most people seem to think aircraft designing is somehow romantic. In reality it can be boring, frustrating & downright hard work.
You don't say which sim you would be designing for. This is important before giving specific advice on the various options & available design programs. These will cost you except for Gmax which is only suitable for CFS2, FS2002 & CFS3 so far.
I would suggest making yourself familiar with all aspects of the sim structure before thinking about designing an aircraft yourself. Have a go at all the other disciplines you will need to know. Creating the visual model is only a small part of it. Any self-respecting aircraft designer needs to know all about repainting textures, editing panels, AIR & DP files & so many other little tricks. There are many free programs posted in the design sections to practice these skills.
Please don't think I'm trying to discourage you. If you're set on taking the plunge, tell us which sim this is for & I'll try to help. If it involves programs I'm not familiar with, I'm sure someone else will jump in.