Using 9.3.1, you'll have to upload the shapefiles individually to create feature services. The feature services can then be added to a web map and symbolized as you need them to be. You can pan, zoom in, and access Esri basemaps for your web map. You can also create web applications using the templates provided that can be embedded in a website. Anyway, since you have 9.3.1, you can't simply upload a whole project that can be accessed through a web map; that can only be done through 10.1.
If you had any version of ArcGIS Server, you can upload your map services to ArcGIS Online that are served from your ArcGIS Server. These can be stored in your My Content section and shared with everyone or specific groups, and can be done if you have a subscription account or simply a personal account. It's a good way to distribute data to the public as they can create their own maps using the public services through ArcGIS Online.
