For a small project I need to utilize a simple database with very light requirements: few tables, no more than few thousands of records in total, 2 or 3 users. I am working
When going with a network share I would go with a network enabled database (mysql/firebird/mssql) instead of access.
For the situation your describing using Access wouldn't be a problem.
I have used Access in more challenging situations then this mostly when working with websites when Access isn't abused beyond measure it really isn't that bad of a database engine. (not talking about forms and stuff like that just tables and records)
When your doing inserts/updates/deletes from several users at once then it gets a bit hairy. This is the point where you start to think about real database engines.
Also when you want a low overhead database which is thread safe you can have a look at vistadb (slower then access, not always free, 100% .NET)
I think access uses table level locks with some kind of queeing mechanism things should work ok. If your worried about it you can always throw a simulated stress test at it.