Transportation Czech and beyond

1. Both take about the same time. Bus is slightly cheaper. I would recommend Student Agency so called Yellow bus. It's luxurious bus with service and bathroom. On Friday and Sunday afternoons I would rather take a train because of traffic jams around Brno and especially Prague. Once it took me 5 hours instead of two and half.
   
2. Train or Yellow bus. About the same time, bus somewhat cheaper. Book bus ahead, also for Prague to Brno.
3. On the top of this page click on Favorite Links and look under Air Travel.

Vienna to Paris via air would be either on Niki Air, Austrian Airlines or Air France.

I checked flyNiki.com and their 1 way flight on 7/22/2014 is $214.

Good luck.

What is the best website to use for the train from Brno to Vienna?
Also what stops do insert to leave the correct station and arrive at the correct station?

Thank you!

The best website for trains in Europe is Deutsche Bahn. You can get to it via Favorite Links at the top of this page. You can also use czech website (it's in English, too). You find train and bus schedules there: http://www.idos.cz

Here is Rick's tutorial for using the Deutsche Bahn website: http://www.ricksteves.com/plan/tips/db_tips.htm. You'll see that if you just put in the city names, you usually don't have to specify a station, and will then be shown which ones the trains use (for most city pairs, there's only one station used in each city, but of course there are exceptions).

I second Ilja for the Student Agency recommendation.
I took a bus from Prague to Brno to Bratislava last month and had a wonderful experience.
Cheap. Confortable. Free coffee. Restrooms. On time. Nice hostess. Free earphones and recent movies to watch. Wifi. Great little trip.