All current generation iPod models (except the shufle of course) can be connected to the TV to watch video.
Also, you should keep in mind that for all recent models of computers,you can directly hook up the computer to your tv to watch video. You dont need an iPod just to watch video on the TV.
a. iPod Nano:
Advantages: -
1. Most compact and light weight. You can wear it in an armband when you run or are at the gym and it is the least obtrusive model.
2. Least pricy.
3. Has a built in video camera.
Disadvantages:-
1. Smaller screen than the Touch (I watch movies or TV series episodes on my Nano on flights or long drives)
2. Lower capacity - If you have a lot of media, you will need to maintain the library on the computer and swap content onto and off the iPod. Personally, I think 16 GB (capacity of the iPod Nano is 8 GB or 16 GB) is plenty for most people.
Most suited if: Listening to music and audiobooks / podcasts while at the gym or working out is the top priority. IT you want to take a few Cathe workout download videos to use in a hotel room with you when you travel, you can still achieve this with the Nano if you get the cable to connect to a TV.
b. iPod Touch
Advantages:
1. Larger screen
2. Wi-fi enabled. You can check email or facebook or buy stuff from the itunes store directly from your iTouch as long as you are in a wi-fi hotspot such as starbucks or in the airport
3. Uber cool touch interface.
Disadvantages:
1. Bulkier than the iPod Nano, though plenty of people run with it and wear it on an armband too.
2. You may want to check out the
iPad whcih has an even larger screen and the ability to read books (like the kindle) which will be launched in March. At the gym, you will not be able to wear it on your person ofcourse, but you can still get a pair of bluetooth headphones and still use it without being attached to it by wires.
Most suited if: Watching video directly from the device or the other cool features of the iTouch are things you will use often.
c. iPod Classic
Small screen like the iPod Nano. But large enough to hold a LOT of content. If you are one of tghe people who wants ALL your videos and music and audiobooks and podcasts on your device at all times, this is something to consider.
Personally, if I did not have an iPod yet, and price were not a factor, I'd get the iPad and a pair of bluetooth headphones to use at the gym.