I think it really depends on several factors, such as scalability, usability and your knowledge of different programming languages or softwares. You are basically describing a CRM (Customer Relationship Management) tool. As far as usability, I find that web based CRMs are much easier to use and access. You are able to maintain the database from anywhere in the world (even underwater these days). One of the other bonuses to web based CRMs is that there are TONS of them out there already programmed. For instance, Sugar, XRMS, PHPCollab, all of which are open source. At that point it is just a matter of finding one that gives you the options you need - most of them have demos where you can go in and play with the application a little bit before you install. With Access, you are limiting yourself to one file, maybe it's on your computer, maybe it's on a server somewhere (which of course must be Windows), etc. If cost is an issue, then you also have to figure that time is an issue as well (time = money). Therefore, in my opinion, it makes more sense to look into an open source (or even if you have to spend $100 to get it just right) web based CRM. The only downside is scalability, in the sense that in Access, it is fairly easy to add new columns or tables and join them and sort of re-route everything, whereas with a web based CRM, you are having to depend on either your own expertise, someone else's, or completely re-rendering the application.
Questions:
Do you have direct/remote access to a server? If so, what platform (Linux/Windows)? On a scale of 1-10, what is your knowledge of programming? And if any, what programming languages are you familiar with? Are you more comfortable using desktop applications (i.e. Excel, Access) or web based (i.e. blogging tools, file sharing)?