I want to make my website look spiffy. Should I use jQuery, or what is better suited to be paired with ASP.net?
I've can say this with confidence - you can use jQuery with .NET with no issues. I do this all the time.
Absolutely. I don't know that it will necessarily make it spiffy as you asked, but it'll certainly ease your programming work.
AJAX will help with the "spiffiness".
You want really spiffy? Look at Silverlight!
Yes, you can definitely use JQuery for ASP.NET apps. Check out an introductory article on how to get started - Getting Started with JQuery
jQuery works as well with ASP.NET as with any other server platform, because it's just a set of client-side scripts. When you consider its daily usage (such as assigning Thread.CurrentThread.CurrentCulture.DateTimeFormat to jQuery calendar) the final code won't look as short and elegant as advertised. The server controls of ASP.NET AJAX have their own bonuses. In short: if you use ASP.NET and not going to change the platform try standard ASP.NET AJAX facility (possibly with AJAX Control Toolkit). Otherwise starting with jQuery can be much better investment.
This link may help you better,
Introduction to jQuery in ASP.Net and 10 Advantages to Choose jQuery