How many more records can I add before Access croaks?

I am a webamster who is decent with ASP but has just recently learned how to connect to databases. I have built a simple inventory display site for my company with about 6,000 records in MS Access. It works well, and management wants to dump 20,000 more records in the database and tell an additional 3,000 people it exists on Tuesday.

Here are some other scenario notes:
-password protected site
-data is FTPed to the site once every morning.
-users do not alter any records, only make searches and view results.
-we are on an $18.95/month shared server from an external webhost
-I doubt we have had more than 100-200 unique visitors in an 8-hour period thus far.

Am I being overly concerned that we need to move to SQL? I have heard that after 10,000 records, Access begins to suffer performance dropoffs or crash altogether. Should we be thinking about an upgrade? How many records can Access hold before we should switch?