If you've got USB2 then an external one will probably work OK - an internal one is probably cheaper.
"would i be able to play those in my normal DVD player attached to the TV?"
would you be able to play what exactly? - DVDs that you create? - yes, usually - depends on your DVD/TV plaer somewhat.
"would the software change other formats to one that the DVD player attached to the TV can play" - There's lots of software around that you can use to change formats - some OK, some not very good. If you do a Google on software video format converters, you'll get lots of software and some good articles to read. It isn't as easy as falling off a log!