Forget the Pentium4. It's a battery hog, and runs rather hot. Two very bad things with laptops.
Pentium M or Centrino chips are good choices. They were designed from the ground up to be mobile chips, so that means longer battery life and less heat.
Core Duo chips are very new, so hard to say. The major selling point is that they're dual core chips, or essentially two CPUs in one. The core solo is the single core version. Core Duo chips might be worthwhile if you're looking to try and future proof the system as much as possible, though for most of the system's life, that extra core is probably going to be more of a drain on the battery than anything.
One other option is Athlon64 or Turin based chips from AMD. On the desktop side of things, AMD has been trouncing Intel for some time now in the bang per buck arena, offering better performing chips at lower prices. I can't honestly say how well their mobile line compares, but it might be worth looking into. My guess would be that they stack up competitively against Intel's offerings on heat and battery drain, while likely keeping the performance edge. Maybe someone else here can offer up an opinion on these.
On a laptop, the main things you will want to concern yourself with are heat dissipation, battery life and overall performance, in that order.
I am a medical transcriptionist and work via my company's platform over the internet, so I am constantly online (high speed). I want to buy a laptop to work off of when I am away from home. I also want to be able to burn DVDs and CDs off of it. I'm looking to get something with at leat 2GB RAM and 100 GB HD. My question is about the processor for this computer. I am so confused about what to look for and what would be best for what I am needing to do. Pentium 4 with hyper-threading, Pentium M, or Duo Core? I want whatever if the fastest, and I can't make heads nor tails of anything about these processors. It looks like greek to me. Please give me some advice! Thank you.