1.) The new Photoshop Elements ($100 or so) has gotten to the point where it's damn near identical to Photoshop. Yes, there's some
bells and whistles you won't be getting, but most of those are features that 90% of home consumers don't even use with the full version.
2.) Is the laptop going to be the only computer you install it on? If so, PLEASE make sure you check the system requirements. I don't think too many graphics apps past 2005 or 2006 will run properly on it, if at all.
Now that I've mocked your computer
(I'm not really -- Just being funny) here's the good news -- you can find pretty cheap copies of Photoshop 3.0 and Photoshop 4.0, especially for the PC. Those should be old enough they run on your laptop, and be cheap ($50-ish) to boot. (I would suggest Amazon or eBay. Amazon may run about $20 more, but there doesn't seem to be a plethora of normal Photoshops for sale on eBay. Stay away from Photoshop LE. If you think Photoshop Elements might be your thing, try to find the highest version you can that would run on your machine)
Some on Amazon: Amazon.com: Adobe Photoshop 4.0 for Windows:...
If you can manage 4.0, go for it. PS 3.0 wasn't bad per se, but is a little too pedestrian when compared to the newer versions.
(I've used Photoshop from 2.0 until the newest version on CS5 and I've been a graphic designer for 11 years.)