The "M" just means that this processor was designed specifically for notebooks - the "M" stands for Mobile. This is a chip that uses less power to help increase battery life. It also has some other features that are more useful for laptops versus a desktop.
A 1.8Ghz processor should be just fine for normal word processing, web surfing, email, etc. And most Powerpoint presentations and DVDs should play just fine. If your PowerPoint uses a lot of transitions and special effects, it might lag a few seconds between pages.
512MB of memory is the bare minimum for running Windows XP. Personally, I would want to upgrade to at least 1GB. So, I would figure that into the price. Depending of the type of memory used, it could cost $15 - $50 for 512MB more of memory.
Integrated wireless means just that - the wireless card is built into the laptop. There is no need for a seperate wireless card.
With most used laptops, the battery is the first thing to go - they only last on average 1 1/2 to 2 years. So, most vendors won't guarantee battery life - you might get a perfectly good battery that lasts for 2+ hours or you might get one that lasts just a couple of minutes. So, if battery life is that important to you, consider buying a new/reconditioned battery for whatever used laptop you end up buying. Hopefully someone from TechSoup can address the battery issue directly.