First of all, yes, an external HDD is a great solution for keeping backup copies of files off your computer. I'd suggest if you are nervous about corruption, etc., you do this: only connect the external to computer when you are making or recovering backups. Otherwise unplug from computer and turn off the power on the exteranl drive.
It's true, eSATA will be faster than USB2. Howver, I'll suggest that Firewire 400 (aka IEEE 1394a) may be just as fast as eSATA.
Problem I can foresee is you may not have an eSATA port on your laptop, and maybe not even Firewire. You may be limited to USB2. If you have Firewire but no eSATA, use the Firewire.
If you have Firewire or eSATA to use, consider this in purchasing the external. Most such units come with at least two interfaces to the computer: USB2 plus one other (sometimed two others). Get one that has both the interface you plan to use plus USB2. That way, no matter what computer you hook up to, there's always going to be a way to attach.
The only externals I know of that do NOT need their own power supply are the ones based on smaller 2.5" drives used in laptops. Virtually all the larger 3.5" drive-based units need enough power to run the drive that it is hard to get it from the USB port. I have two preferences here: I like the externals with their own power supplies anyway, to minimize demand on the computer's power system. But going to the larger drive form means two advantages: you can get larger capacities this way, and for the same capacity the smaller 2.5" HDD's designed for laptops are 'way more expensive. However, I must agree that the smaller ones designed for portability with laptops are easier to pack up and carry around.
To go with my desktop I bought an external case and HDD separately, put them together and voila! That is a bit less expensive than buying a ready-to-go External Hard Drive unit, and you can customize it. Just remember to get BOTH interfaces on the external case chosen correctly. Besides deciding the case-to-compouter interface(s) (USB2 plus Firewire, for example), you need a case that uses the correct connection to the HDD you plan to mount in it - SATA (Usually SATAII these days) or IDE.
But, if you don't want to customize and roll your own, buying a complete ready-to-go unit also works well. You may even get with it some freebie goodies like a CD of backup / restore utilities.