I hate to say this, BUT. I suspect that your supervisor's expectations may be unnaturally high, particularly when: "The guys here don't really know what they want". All those things you propose to do can be done, given the time and expertise and MORE, including serving the data on the web if there is a need to present it to customers in an interactive format. Print out and give this note to them if it helps in your efforts.
This is definitely feasible - depending upon how good you are in dealing with relatively steep learning curves. Learning GIS, its concepts and individual software issues can be daunting. Are you willing to work double shifts? The 2 month time frame is problematic.
First, get online to ESRI's website and search for all the white papers dealing with this subject (read in association with all your other tasks - These can go a long way in answering the 'what the software can do ' question - you interpret from what is left out as to what it CAN'T DO. Here: http://support.esri.com/index.cfm?fa=knowledgeBase.gateway
The FORUM for Utillities/Wastewater may give you some help, here: http://forums.esri.com/forums.asp?c=140&dy=365, OR http://forums.esri.com/forums.asp?c=141.
The Industries section (water/wastewater) may give you some help, here: http://www.esri.com/industries/water/index.html
Data modelling and using pre-built data models is an important factor when using the ArcMap suite - if you have the EDITOR or INFO license. If you only have the base ArcView license, forget about the whole modelling idea - for now, you don't need it anyway.
- Definitely go through the exercises in the book/documentation and I MEAN actually do the exercises, don't just read them. This will give you at least a beginning knowledge of the how the software works. (Don't have it? You should. Some books usually ship with the software. The others can be downloaded from the program discs in the Documents section as PDF files.
- It would be great if you can get the basic files from the county in digital format (CAD or GIS) then re-create your paper maps as a new layer over the top of these. If not, you'll probably have to resort to scanning and digitizing on screen - but this is another issue.
- If you don't have the advanced licenses, create you work as ESRI style shapefiles; these are easier to work with than the 'Personal Geodatabase' for beginners.
- Learn about FEATURE ATTRIBUTES and how to get them into the associated shapefile table. Once you have the features in GIS style, then you can work with them to some degree such as displaying them with different linetypes, lineweights, color, etc. for each type of feature in the piping run: age, size, valve, valve type, bends, etc.
- As for modelling, though, it is tough to do real modelling with the base install. Just learning how to use the Data Modelling Tools in ArcMap is a subject of its own.
Finally, I don't intend this diatribe to be a 'damper' to your hopes - but reality plays a big role. I sincerely think that you need to sit down with your bosses and tell them that the best they can expect in this short a time is to just get the map(s) into GIS format - this will take much longer than you or they would believe! Don't forget that you need to learn how to do it too!
When you have convinced your bosses to go ahead with this project (and it sounds like it needs to be done), to let you start the project - even if someone else finishes it, then start reposting on ESRI's Forums your questions. There are many professionals and beginners like yourself who can give you all the assistance you'll ever need. Much better than any book!