LET'S TALK TROMBONES

It depends, in my opinion, on you level and your dedication. If you are just starting out and are buying your first trombone I'd suggest buying a new trombone.
If you have played a couple of years and know how everything is supposed to work you can find a good deal on a used instrument on places like eBay or Craigslist. 

If you are just starting out and are not sure you'll continue playing it might make sense to rent. If you have just a small amount of dedication to trombone playing I'll strongly suggest buying a horn. 
There are cheap horn available that you'll be able to sell at a  not-so-great loss.

If there is a (professional) trombone player in your city, call him/her and ask for lessons. No matter how you spin it 1 on 1 lessons in person, is the best option. 
If that is not possible for you, there are online music schools where you'll be able to find a teacher. 

There are benefits to both student and professional trombones. 
Student models are generally easier to play while professional horns offer more depth of sound and are of a much higher overall quality.
If you are just starting out go with a student model.

Prices range from around $200 to $10,000.
Trombones are quite simple to produce compared to other instruments and are comparably cheaper. 

Just know that you get what you pay for. Don't buy a $200 trombone and expect to sound like a professional. 

Read all about the cost of a trombone here

Well, a case or a gig bag are nice to have if you plan on playing with others (and you most definitely should do that). 
A music stand is also nice.

YES! :-)

You don't have to.
I have played trombone professionally for 20+ years but opinions expressed on this page are just that: my opinion.