My advice is to take the P2 only if you can get it for a song - meaning like somewhere around $100 or less. In my opinion, a P2 is simply too slow to be practical with any modern software. My advice would be to take the laptop if you want it, but expect to purchase a new one when you start in college 1-2 years from now.
It's simply impossible to find a campus today that is *not* expecting students to use some sort of internet-based information system. I use my laptop (Sony R505 "SuperSlim") extensively in my upper division classes. Homework, team collaboration, grading, registration, calendars, etc. etc. are being conducted with greater frequency on the internet. Expect to find CD-ROMs bundled with many of your textbooks. MS Office XP is included as part of the tuition on our campus - on top of that, add in any graphics, math analysis software, groupware, anything bundled with a textbook, and stuff you get from friends.
One of the most common mistakes I see people make when getting a laptop is underestimating the power that they need to get the job done. You can easily spot these people in a lab, the ones who are spending most of their time fiddling with old network drivers, software incompatibilities with obsolete hardware, insufficient RAM/HD space, not enough CPU power to run Java, etc. etc. instead of getting their work done.
Another thing is that laptops are made much lighter and thinner than they used to be. It's not uncommon to find some older models tipping the scales around 8-9 lbs. In itself not a big deal, but when you add the rest of your books and a 300-400 acre campus, it can be unbearable for more than a short walk.
The most important consideration in my opinion, should be the WEIGHT. Try to get the slimmest, lightest machine you can afford (Mine is 3.5 lbs.). Beware of cheap laptop prices - the rule of thumb is that the lower the price, the heavier the laptop. A laptop weighing between 2-3 lbs. should start at around $1500 and would be considered "lightweight". 3-5 lbs. is your "middleweight" laptop starting somewhere in the neighborhood of $1300. 5-7+ lbs. is considered a "heavyweight" and should start around $1000.
If you want to be able to play games on the road, you should look for either Mobility Radeon, or GeForce Go video chipset. Expect to find this chipset only in higher priced, and heavier laptops. If you commute a long distance to campus, you may find yourself with several hours to burn between classes from time to time - being able to fire up the latest 3D game can really make the time fly.
I hope some of this info is useful to you. Be sure to apply for Financial Aid when you make the college jump - you might be surprised to find that the cost of attending your school (including the cool technology) has been included in your aid award.
Good Luck!