I would like to send text messages that are easy to send and receive on my desktop. Or a web app, add in, whatever works.
looking for desktop texting
I've had good luck with Google Voice (free!) - it seems to be the most complete solution. You get a free phone number in the area code of your choosing, which you can even forward to a landline or cell phone for calls. Should you have an iDevice of some sort, Google has a free app to enable texting with your Voice account on that as well. There's also an unofficial desktop app that runs on Adobe AIR, but the web-based interface is just as good in my opinion.
You can use Uppidy.com to store your texts for free but I am not sure about texting from your desktop for free.
You might try using a service such as Text 'Em, which lets you send and receive SMS messages online. I believe you can send without signing up, but have to create an account on their site to receive messages.