Hi AngieLynch,
Thanks for visiting Apple Support Communities.
It sounds like you're seeing some unexpected behavior in Mail.
Before troubleshooting on your computer, I'd strongly recommend backing up your data to an external hard drive with Time Machine, if you haven't already. This article can help with setting up Time Machine:
Mac Basics: Time Machine backs up your Mac
http://support.apple.com/kb/ht1427
Next, try creating a new user account on your computer. You can add your email account to Mail in the new user account. If Mail is more responsive in the new user account, then Mavericks is working fine and the behavior is caused by conflicts in your own Mail or user account.
These articles walk you through creating a new user and setting up Mail:
OS X Mountain Lion: Create a new user account (applies to Mavericks, too.)
http://support.apple.com/kb/PH11468
Configuring Mail for your email account
http://support.apple.com/kb/HT1277
Best,
Jeremy