I happened to glance at this question when it was at the top of the page and felt I might be able to clarify a little bit. It wasn't entirely clear if the user who originally asked the question had an answer that was clear. For the benefit of any others who might have this issue as well, I wanted to see if further input might help.
Question: Does the Late 2007 MacBook support the latest version of OS X (Mavericks)?
Further, if not, what is the latest version that it does support and how can I go about attaining it?
Simple Answer: No. Unfortunately, your system will not support OS X Mavericks. The most recent version of OS X that you can install is Lion.
Detailed Answer: From your question, I gathered that you already have the Mac App Store. If that is correct, you can purchase OS X Lion by calling 1-800-MY-APPLE for $19.99. You will get a content code that you redeem in the Mac App Store that will allow you to download and install the upgrade.
Advice: I kept my 2006 MacBook Pro for 6 years before upgrading. At that point, the $3000 investment had cost less than $500 per year. That's like buying a low-end laptop that's never as user-friendly and making the transition every single year. At the end of those 6 years it was still a very capable computer. With any Mac of its age that is still in use, it is typically safe to presume that it has served its purpose well for many years.
That said, the reason we look to upgrades like SSD's and our OS is because the the content that we are consuming is becoming more life like and intuitive. As the content grows larger and more complex the platform that you use to view it has to advance with it. As the platform, be it a plug in like Adobe Flash or your entire operating system, is advancing the hardware has to work harder to keep up.
That concept is rather simple, if not for technical reasons then because it's a life cycle we've all experienced with all the products we buy throughout our lives. The missing link, I believe, develops in the many layers between what we eventually consume and the hardware that enables it.
Your MacBook is, effectively, as up to date as it will ever be from a hardware standpoint. You can't upgrade the processor, you have the most memory your system supports, and you've upgraded to an SSD. From a software standpoint, you're able to take a step forward but even then it's to an operating system that is no longer supported with updates that help it change and adapt to the ever changing content it is used to consume and the ever evolving threats that may be encountered to get in the way.
It's safe to say that your Mac is, fortunately yet unfortunately, living past the end of its product lifecycle. As the content, plug-ins, and OS's continue to advance, your system is no longer able to adapt and maintain compatibility. If all that you use the system for is to interact with the current versions of the applications that are on it, I've encountered individuals who are still using Mac hardware over 12 years old. With regard to content from the internet, however, the portion that your system can access will only decrease from here on out.
So one can assume that you most likely got years of above average performance from a system that has turned out to be quite a value. Although now might not be the best time to consider doing so, replacing it will be a better value for your money and definitely your time. While you might now be able to buy a new Mac for less than $800, the broad majority of tasks you may have performed on the MacBook are possible on a $500 iPad. A new iPad has the benefit of being more portable, more powerful, and built with today in mind.
Just some food for thought. I hope that I was able to be helpful.