Monitor with TV input jack

I want to use my monitor not only for my computer, but also to watch TV. Am I better off getting a 27" 1920x1080 monitor that also has a TV input jack (is there such a thing?), or should I be looking for a 1080p TV and connect my computer to the tv instead? Thanks for any help.

$400 budget.
 
Solution
TV will have speakers, more inputs and a tuner. However, they tend to have slightly more input lag, which isn't good for gaming.

I'd get a standard monitor, then get a PCIe tuner card. That will also let you do cool stuff like fast-forward through ads, and makes it easier to record.
TV will have speakers, more inputs and a tuner. However, they tend to have slightly more input lag, which isn't good for gaming.

I'd get a standard monitor, then get a PCIe tuner card. That will also let you do cool stuff like fast-forward through ads, and makes it easier to record.
 
Solution