Rather than buy a skilsaw, you could ask to borrow one from a friend. In my small circle of friends, I probably could borrow over a dozen of them for a day or two. That way if you end up not enjoying it, you aren't out the cost of a skilsaw.
I say this because tools are like many things in life and you get what you pay for. If you buy a cheap one, it might work for this project but if you soon get serious about woodworking, you will wish you had a better one. If you get the better one right off the bat, you will have to pay more up front making the cheap DIY bookshelf project not so cheap if it is the only one you do. I have a nice skilsaw and a router (I actually have two routers) in my shop and they are two of my hardest working tools for around the house projects.