Sorry, I have a tendency to scan through walls of text - a bad habit I need to break.
I would not get the best money could buy. From a monentary stand point you are throwing your money away. The depreciation is worse than new cars.
$3,000 for a laptop is just way too much. $1,800 would be the max I would spend on one. While 7 years from now (like the laptop I'm using) it won't have the battery life nor the power but you will still have a nice laptop to browse the web, check e-mail, and what not. This computer runs Maple 13 like a charm and I only have 1.5gigs of RAM on it. Of course I haven't tried anything horribly computation heavy.
One way I build computers/look for specs is get a new high graphics game and look at the required specs. Really processing power isn't much of an issue even at the dual core mark but RAM is. You may be a little hard pressed to fit 8 gigs in a laptop but I know they make em. http://www.newegg.com/Product/Product.aspx?Item=N82E16834220704 Out of stock....but that's basically what you are looking for.