You are exactly rite about the recordset, but you would want to make sure it is on the page that your checkout form posts to, so check the action on the form for that.
Once the recordset is in place you will then be able to create a new session variable, you can do this by going to Server Behaviors > eCart > General > set session value. For the trigger you can use the posted element for the county. For the value of this session variable you will set use the lightning bolt icon to expand the bindings for your newly created recordset. In here you will select the column that holds the tax rate.
That should ensure that you are setting the session variable accordingly. You can then use this session variable as a trigger for the charge rule. In the rule you will first create the trigger, for the condition in the trigger you would select 'session variable exists' then select this session variable. Then for the amount you would use based on cart subtotal and use the subtotal times your session variable name for the total amount of the charge. For this part you must enter the name of the session variable just as it was set like this:
If you set it up like this it should dynamically apply the county tax charge based on the selection of the user. If you have any trouble with this or need some more info let us know and we will be glad to help with whatever we can.