It really doesn't make much difference what make you use - all are reasonably OK performance wise these days (especially for backups). External drive prices really haven't followed the hikes in bare drive prices - at work we've recently bought some external drives and removed the cases to get drives for a customer project !
The main choice is to capacity (bigger is better !), and interface. It would help to know the model of Mac and what ports it has. Until relatively recently, all Macs had Firewire (some of them Firewire 800) and contrary to what people say, Firewire at 400Mbps is actually faster than USB2 at 480Mbps due to architectural differences. Firewire 800 even more so. Also, Firewire can supply more power (12W) than USB (2.5W) and you get a better choice of drives powered from the computer. eSATA is much faster still if your computer has it.
Older Macs only have USB1.1 which at 12Mbps is really slow - so if you have one of these then definitely go for Firewire.
Aim for your backup to be at least twice the size of your main disk (or at least twice the size of your data) and you'll get a lot of backups going back some time on it (but obviously not going back before you started, Time Machine isn't
that good

)
Most drives will come either unformatted, or worse, formatted with a PC filesystem (either FAT32 or possibly NTFS for really big drives). Use Disk Utility to change this and use HFS (Journaled) which is the Macs native filesystem
Lastly, remember that although Time Machine is infinitely better than the backups most people don't have a all, it's still an "all eggs in one basket" situation. If someone breaks in and nicks your Mac, or the house burns down, then your backup is likely to go with it.
The easiest way to deal with that is to use an online backup system as suggested, or buy two drives.
With two drives, leave one at a trusted friends house and swap them round every so often. You'll have to go into Time Machine and tell it to switch drives each time, but you'll have a copy of your stuff off-site if the worst happens.
it is of course possible for the backup drive to fail or for the data on it to get corrupted. Such a second drive would give you some protection from that as well.
The biggest downside is that you won't have all your backups available - ie there'll be gaps in what Time Machine can show you.
Of course, you could go OTT like me. As well as using Time Machine, I have an old Mac in the back room (along with my other servers) which runs
Retrospect and backs up all the computers in the house. For that, I have four hard drives (used to use tapes) and at any time have two at work and two at home which get rotated. So generally I have 3 or 4 copies of all my data, 2 of which are in the office. But then I've been responsible for backups for several employers over the years, so I'm somewhat more attuned to the requirements and risks than the average home user.