Hey Bulldog,
there's no performance hit going to a laptop vs PC, however if you're looking to add in components to your unit, i.e. video card, specialty cards for audio, etc then a PC is the way to go. As Flopnfly said the convenience of the laptop is much better, as you're not stuck to one area with it, and with the processing power in the CPU's today it will be as fast as the PC. Video on laptops for the most part is not as good as some of the higher end cards that you can get for PC's for gaming and such, but, for most users it won't make that much of a difference, however if you're a purist, then it would be consideration.
A few things to look at either way:
1) memory is cheap today, and all software (especially Windows) is memory hungry. The more you can put into your machine, the better. My recommendation is to go with at least 1Gb now, 2 if you can get it for a good price. (from the top of my head a 1Gb upgrade today is about $170-$200 roughly).
2) disk space. Hard disk space is cheap today, so you can easily look at 100-150 Gb hard drives for laptops and upto 500Gb hard drives for PC's (even more if you want to be on the bleeding edge). The thing to remember here is that you want to back that up somehow. The easiest way, without springing for another system to act as a "server" or "backup machine" is to get an external USB hard drive, perferably at least the same size as the hard drive on your computer, more if possible. They are pretty inexpensive now, as future shop or bestbuy have the 250Gb External drives for about $170.
3) CD/DVD. DVD is pretty much the standard now, so getting a dvd player/writer will allow you to read and write both CD and DVD. (big change from 6 months ago!) If it's not in the base package, it shouldn't add anymore than about $100 to the price.
As for the question about leaving it on or off? well, turning it off ultimately is a better idea, for many reasons, (clearing memory so that it runs faster, power consumption, wear and tear, etc) but it won't do that much harm in leaving it on as well.
hope that helps a bit
