Much have been said already, but here is even more encouragememt

:
Like mentioned, you are actually already taking steps outside your comfortzone by planning this and writing here and everything! That is awesome!
I've both played several open mic nights and been busking in a couple different contries, and if I were you I'd maybe try an open mic first, for these reasons (from my experience at least):
In most cases weekly/monthly open mic night arrangements are very happy to see more people show up to play to keep it alive/going. They will probably be very nice and helpful, especially if you mention it's your first time and they will help you get your guitar plugged in right etc.
There will most likely be alot of people there just like you - kind of nervous, but wanting to play, some planning to play, someone just watching for now. This makes for a supporting atmosphere which is very nice for everyone involved. Maybe you will help someone take the leap and play a song next time?

It never rains indoor, and the temperature is usually comfortable.
It has a clear start and end. You start, play one or three songs, and you are done.
(But if busking is more appealing to you, do that!

Or why not just try both?)
Now, some general thoughts:
No matter what you choose and how it goes, you will not fail.
No matter what happens, you will grow as a person.
No matter what happens, if your intent is to create art for others to enjoy at the best of your abillities, and also forcing yourself far outside your comfort zone while doing so, you are a godamn hero dude, and stronger than most.
Feel free to contact me if you have any specific questions regarding anything about playing live, I'll be happy to help.
