This sounds like a great idea! I did some research and found a few other companies offering similar services. One is called Realty Video Tour: http://www.realtyvideotour.net/ They seem to have a nice template put together where they are able to combine their interior video with some custom music but to me, their prices are a bit low for what they're offering. However, they are quite competitive! They seem to be using a consumer model HD camcorder for their services.
Another is called AgentCasts: http://www.agentcasts.com/ They have some easy listening style music in their videos along with a very good narrator talking about the finer parts of the home. If the picture on the home page of their website is any indication, it looks as if they are filming their productions on a Sony DCR-VX2100 DV camcorder (in SD). I wouldn't recommend this since most people will likely want their production done in HD (psychologically it makes clients feel better about your services) and since tape takes a while to digitize, but I will say their prices are at least more along the lines of what I would expect.
With these websites in mind, and with my own assumptions about what you would need included, I would recommend a camcorder like the Canon Vixia HF M40. The reason I would pick this camcorder is because it fits your budget ($350 on Amazon), has a larger image sensor (1/3 inch rather than 1/4), records to an affordable SD card, has a wide angle lens (at 43mm), and has an onboard memory of 16 GB. In addition, the camcorder records in both an MP4 and AVCHD mode which will both work smoothly in Adobe Premiere Elements. If you did get this camcorder, I would buy the optional bigger battery the BP-819 in order to get more recording time. You never know how long these shoots might take you – especially in a large home!