When price is the determining factor, you have to do the best you can for what you can afford. I've always been in that position, but I must say I've done fine with laptops despite their low endedness.
I won't mention the Packard Bell piece of junk I got in 1993. It was an awful computer but it was all I could afford and it worked for five years. I replaced it with a Fujitsu Lifebook in 1998 (P133, 48 megs RAM, 6 gig hard drive). I ran VectorLinux on it and it was rather painful but it worked.
In 2003 I got a Toshiba Mobile Celeron 2 GHz with 512 megs of RAM and a 40-gig hard drive (a typical size for the time). It has Intel shared graphics, which work fine in Linux, except it couldn't do 3D until VL 5.9 and even with 5.9 I have to use the vesa driver. The Intel driver works--until I reboot. Then the text on the desktop turns a light transparent grey and is almost invisible. With the vesa driver things work, but the glxgears scores are miserable. That computer is now working daily on our hall desktop and we call it my husband's computer, except he rarely uses it.
In August 2007 I got a Gateway Turion that's all-NVIDIA inside. I expected Linux would be a piece of cake on it, but it wasn't. The graphics always worked fine, as did the Ethernet. I was never able to get sound under VL 5.8 and couldn't get the Realtek wireless to connect after I got a wireless access point. It was a real struggle through a few betas for 5.9, but eventually Uelsk8s and others got everything fixed up and now everything is working fine and I do have 3D with the proprietary NVIDIA drivers.
I would't worry about onboard graphics. I've had them on two Linux laptops and one desktop without problems. Intel-hda audio, quite common on laptops today, can be a challenge, too, but it's working fine on my Gateway now.
I always use my laptops on AC power, so I have no experience with Vector's power management. I also don't hibernate or suspend. But video, sound, networking, printing, and dual booting have been fine on the old Toshiba from the start and on the Gateway after a fair amount of work.
Some of the big box stores will let you return the machine within a 2-week or so time frame for any reason without a restocking fee. I think that's Staples' policy; I don't know about Best Buy. I bought my Toshiba at Best Buy and my Gateway at Circuit City. They happened to have the best sale price at the time I needed to buy. If the return policy is favorable, you could install VL right away and see if everything is working. If something isn't working, you could use the restore DVD to return the computer to from-the-store condition and return it for something else. If you don't get a restore DVD with the computer, you should be able to make one with a program included with the laptop. Be sure to do this before you mess around with partitioning.
Also be aware that if the computer comes with a gig of RAM and the machine has a 2-gig capacity, both slots are probably filled with 512-meg modules and you'd have to remove them and buy two 1-gig sticks in order to up your memory to 2 gigs. The store will try hard to sell you an extended warranty. It's not a good idea to buy an extended warranty from the store. If you want one, buy it directly from the manufacturer. I used to think an extended warranty was a good idea for laptops because repairs are generally extremely expensive and few users could make a repair except for adding memory and replacing a hard drive. However, those extended warranties cost a LOT and given how inexpensive laptops have become, I think it makes more sense to save your money and buy a new computer if the one you get bites the dust right after the one-year warranty runs out.
By the way, you can *always* find laptops at similar prices, so rather than make a hasty decision if you're not sure what you want, just wait till next week or the week after. They may have an even better deal then.