When finishing the basement, the walls would come first. If you are hanging a suspended ceiling, it would attach (on the edges) to the finished walls, and the floor need only be finished up to the walls.
The first thing to do is to cover your existing exposed foundation walls with a good sealant to make sure you don't have any leakage. Then measure every thing, so that you can make a good blue print for yourself to follow. It wouldn't hurt get a cad program for this need (and believe me there will be some changes before you done). Get a good book if you've never framed before, you'll need to know how to make your corners and there will be some handy stuff you just need to know (believe me you don't want to have to rip stuff down because you didn't have a stud there to support drywall or something.
Unfinished Basement as Storage We're planning on using the unfinished basement as storage for books, papers, clothes, toys, etc. The basement has the oil tank and the thankless water heater. It currently has some seepage due to lack of gutters. Is it safe to use this unfinished basement for storage after we put in the gutters? Or will the inherent dampness of basements cause trouble for the books and clothes? Can I put indoor/outdoor carpeting without finishing the basement? Well, yes, first eliminate the water source. Gutters may be the only thing you need to fix, but maybe there is more. The books etc. will certainly be ruined in the high humidity inherent in a basement unless you lower it with a dehumidifier. You may not need to run it in the winter, but you will definitely need to run it in the summer. (This assumes you have a winter and a summer??) So use the dehumidifier if you store anything down there even if you have NO leakage. As for the carpet, yes indoor/outdoor works best. The dampness and moisture from the floor over time would ruin anything else. Here again though the dehumidifier will help prevent mold and mildew.