When you create a new document, choose the "Web" profile. The setting is sticky from session to session, and will remain at the last profile you chose. All swatch colors are RGB by default in web documents.
If you have a specific set of colors that you want to use in multiple documents, create a dummy document with those colors in the Swatches Panel. Choose
File > Save As Template. Illustrator saves the template in its template directory, which is empty at the top level and contains only a subdirectory of called "Blank Template" that aren't relevant.
Any time you're creating a new document, click
Templates... in the
File > New dialog and load your template with your saved swatches. This is faster than saving out an ASE file, and lets you include gradients and patterns that the ASE format doesn't handle.
If you're doing web work for several different projects, make a named template for each project.