NTSF External Hard Drive Back HELP PLEASE!!!

So I have an external hard drive which I want clean slated and brand new ready to back up my MacBook pro. How should I go about this?
Should I connect it to my new MacBook and format it?
-OR-
Should I connect it to my old PC that it was originally used for? (Hence, NTSF)

What format should I format it to?
Fat32 (I believe it is called) I hear has a 4gig per file limit?

I'm going to want to use the external primarily for backing up my MacBook Pro, however I think there may be times in the future that I am going to need to hook the external up to a PC again.

Thanks everyone.

You have all the important facts to hand there so the choice is really yours.

If it's purely for Mac use I'd say use HFS+. Also if it's to store a backup I'd suggest using it as a didcated Mac drive is the way to go.

If you need PC compatibility then FAT32 will do (file limit exceptions apply, as you noted).

However, I'd suggest NTFS and grabbing a copy of Paragon NTFS for Mac to provide robust read & write under OSX.

The other alternative is to partition the disk (if it's big enough) and go half-and-half PC/Mac.

You could format it to exFat (the 64-bit version of FAT, with a file size limit of something like 16TB, more than you'd ever need on anything short of a server-class RAID array), which should work with all contemporary Macs; but only with the later versions of Windows XP & onwards on PCs.

However, if you're not going to be using it on PCs the Mac default of HFS+ is best (both as it is a superior file system, and because it is the only system that Time Machine will/can write back-ups to, just like how Windows can only back-up to its default of NTFS).