There is currently a shortage of drives due to flooding in one of the countries in which they are manufactured.
Getting one for under $100 at this point might be difficult. You didn't mention how full your current hard drive is, but for Time Machine, you should plan on two to three times the data you currently have (or expect to have).
I looked through Newegg's selection and didn't see more than a couple 1TB drives for less than $100. I recently bought a 3TB drive for $150. They're in the $200-$300 range, now.
I always buy bare drives and put them in an enclosure I buy separately. All the name-brand, ready-to-use drives come with a bunch of software you don't need and some of their software causes problems.
I had some bad luck/bad customer service with Seagate, so I've been buying Western Digital. Though, my replacement drives from Seagate have been going fine.
I've used Icy Dock and MacAlly enclosures. Both have worked well. If you do decide to go that route, you must make sure the enclosure can support the size of drive you buy (both physical--2.5" or 3.5", and storage size--1TB, 2TB, 3TB). The controllers in the cases may not be able to handle a 3TB drive, for example.
No matter how you go, you have to decide what kind of interface you want to use. USB is cheaper, but Firewire is faster. Firewire 800 is even faster, but costs more. All of that depends on what ports you have on the computer. OS X doesn't currently support USB 3.