You could either update the column in the table as you suggested, but if it was me I'd log the event to another table, i.e. id of the record, datetime, userid (maybe ip address etc, browser version etc), just about anything else I could capture and that was even possibly relevant. (For example, 6 months from now your manager decides not only does s/he want to know which records were used the most, s/he wants to know which users are using the most records, or what time of day that usage pattern is etc).
This type of information can be useful for things you've never even thought of down the road, and if it starts to grow large you can always roll-up and prune the table to a smaller one if performance becomes an issue. When possible, I log everything I can. You may never use some of this information, but you'll never wish you didn't have it available down the road and will be impossible to re-create historically.
In terms of making sure the application doesn't slow down, you may want to 'select' the data from within a stored procedure, that also issues the logging command, so that the client is not doing two roundtrips (one for the select, one for the update/insert).
Alternatively, if this is a web application, you could use an async ajax call to issue the logging action which wouldn't slow down the users experience at all.