Since you're talking about jQuery I would like to say, you should use
autocomplete plugin by jQuery[
^]. It allows you to provide it with a list of objects, that you can use as autocomplete values.
If you want it for both, you would add this to both of them. You can also download the list for the second text box from the database; using ajax requests, based on the text in the first text box.
Sample to allow autocomplete is,
<input id="autocomplete" type="text" />
var list = ["One", "Two", "Three"];
$('#autocomplete').autocomplete({
source: list
});
This way, you can set up autocomplete feature for your text boxes (please note that in ASP.NET a text box control is rendered as an input field in the browser for JavaScript; or jQuery, to manipulate it). You can read the link I have attached for more about autocomplete plugin.