A lot depends on the type of camcorder you're going to edit your video from.
As I point out in my books, you're using tape-based video, you can likely get by with a dual-core or i5 processor. But, if you plan to edit AVCHD hi-def video, you'll want to invest in a good quad-core or i7 processor with lots of hard drive space or, even better, a second hard drive.
In fact, I usually recommend against using a laptop for this program. Because laptops tend to cost about 50% more for the same power as desktops, it's likely going to cost you a lot for suitable laptop. Also, since laptops are built for portability rather than speed, you may not get the best performance from a portable system.
I also recommend against getting Windows 7 64-bit if at all possible. You won't get an increased boost in performance from a 64-bit operating system, and conflicts with 32-bit drivers are quite common. So go with the 32-bit version if you can get it.
But, yes, the program is very powerful (up to 99 tracks of audio and video), so you can certainly do the basic audio and video editing you describe.
Finding a laptop for video editing is not easy, as most are ill-suited for that task.
I use a Sager, and it is great. The only complaint that I have is with the 17" monitor, especially as my workstation has dual 21" matched, calibrated Hitachi monitors, and I really love all that screen real estate.
Most newer laptops can be configured for a fast i7 CPU, and an nVidia, or ATI/AMD GPU chip. They can also be configured with ~ 12 GB of RAM. So far, so good. Now comes the biggest rub - the I/O Sub-System. Most laptops ONLY offer a single HDD. Some will allow for 2, and that is the minimum for video editing. I am talking physical HDD's and NOT partitions. The Sagers allow for 3 HDD's, and that is an ideal starting point.
One can also add eSATA externals, to up the HDD capacity, and that would be my second choice, if the laptop that I needed did not offer 3 physical HDD's, like the Sagers do. Even with 3 physical HDD's, the eSATA externals are a bonus. This ARTICLE will give you some background on using externals.
The Sager units are not cheap, but are very well built. I have been using one for 4 years, with no issues, and it's running about 12 hours per day, and is very often used with very large video Projects. I just placed an order for a newer one (much faster, with more RAM, larger internal HDD's and Win7-64 for PrPro CS5). The new unit is also cheaper, than the one that I have now... such is life with computers.
Do not be tempted with features like Crossfire, or SLI, using 2 video GPU chips. PrE (and PrPro) cannot use that, and those setups can really get in the way. Use the $ saved for the 3 HDD's, and as much RAM as you can fit in.
Not sure of other mfgrs., who might offer similar. I have looked at Alienware (now part of Dell), Dell and HP. Some will offer 2 internal HDD's, but only the Sager, per my research, offers the 3x configuration - but that might have changed. All others, like Vario and Toshiba, fall very flat in the hardware areas.
I have a Sony Vaio with i5 processor and 6 GB RAM, 17.3" screen Windows 7 64bit and Premiere works nicely, I handle large full HD videos, no problems at all.
The screen size is something you should take into consideration. Regarding 64 bit keep in mind that not all your existing software may work with it, and that may include camcorder software, printer etc if old. But I'd say 64bit is the way to go.
I'm still at the novice stage having just had Premiere Elements for a week. I would say keep the laptop in-line with your editting ambitions: I tried using basic, free editing software on my 1.3 Ghz / 1MB Ram netbook. Not a chance!
I got Premire Elements on my single core, 2.3Ghz / 3MB Ram laptop ( on Vista) and it has worked seemlessly...but I am only using two tracks of video and audio with ultra basic effects. But this suits me fine.
My point is, there are lots of ways to spend money so if you have the money and the need go for gold. If, like me, you have modest ambitions there are good deals to be had as todays cutting edge technology is tomorrows bargain (I remember seeing a 4Gb memory stick in a camera shop back in 2003 for £400. ) and in this climate it is a buyers market!
I have an Alienware M11X with an i5...they also come with an i7. They are somewhat pricey but I love mine...you'll find an entire forum devoted to this make on the web. I have used my with PE without any problems....