I'm a graphic designer, and one of the first questions I ask my clients is what their budget is for the project. That gives me a really good idea about how much they expect or are willing to spend. I never charge by the hour unless I'm on site or if it's tedious design work where there's no firm finish in site. Once I understand the scope of the project and make a list of everything that is going to be done that will establish the scope of the project (which I'll later use for the contract), I'll then calculate how much time each task is going to take. Right now my rate is $50 an hour, which I can charge because I've been doing this for a few years, have a degree in it, and live in California. When I lived in a small town in Idaho and was still a student, it was about $25 an hour. For things like logos and web sites I do a flat rate because it's easier for clients. I'll try to only work for the hours that I set aside for the project, and if the client tries to ask for new things that are outside of the scope of the project, I'll just point to the contract and say, "it's outside of the scope of the project, but I'll do it for an additional fee." That'll help you from falling into scope creep.
So, ask them what their budget is. That's the best advice I can give right now. Figure out how many hours that will translate into, and then do that much work. There are $100 logos, and there are $1,000,000 logos, and the difference is how much time is spend on it. I use the concept of revisions to explain to clients the difference between cheaper and better logos: number of sketches, number of directions based on those sketches, and number of revisions based on those directions. Since you haven't done a lot of that kind of work you'll probably have a hard time guessing how much time each stage will take, but just be sure to pace yourself. For a small job like this, I bet the sketching phase will take about 3/4 of the time.