First thing's first: make sure that you have a backup of your old system if you need any of the old data. Keep the backup for later.
Hmm. It's a good thing to be doing, replacing your HD. But only do it yourself if you are ABSOLUTELY SURE that you know what you're doing - when you don't, it usually ends badly (I tried and snarled up both HDs I was initially replacing). So be careful. And it looks like your model laptop has a lot more to it than meets the eye. Here's the replacement guide:
MacBook Model A1278 HD Replacement. Just follow those instructions, but instead using the Solid State Drive.
Also, make sure the SSD you bought fits perfectly. Swap it with the HD using the guide I've put in. Now, on startup, hold Command R and select your Wi-Fi Network. Your computer will then download your recovery tools package. This normally takes from 10 mins to half an hour. After the tools have loaded, select Disk Utility. This is to check your new SSD is formatted and has been placed properly. Your new SSD should pop up on the sidebar. If not, consult another guide on how to format it, because that's not my field of expertise! If your SSD has appeared, close Disk Utility, and return to the OS X Utilities pane.
If you want to put your old data on your new SSD, follow these instructions:
Now, this time select Restore From Time Machine Backup. Once you agree to the terms and conditions, plug in your backup drive and select the backup you wish to use.
Alternatively, there is a program the iFixit recommends called SuperDuper, a program that copies your system directly to a new source.
And as for Mavericks? If you have a backup drive, download and install Mavericks and then backup your computer. Otherwise, you'll just have to use the installer disk and go from there.
Whatever you do, it's your choice. Just be careful... hopefully this answered your question. Ask again anytime, and let m know if it goes well.