I would advise contacting established local theatre companies and see what programs they have in place for supporting new writers ie free script readings/writers groups/festivals/rehearsed readings etc.
I had my first play produced after it won a competition, from that I got a commission to write a short play for a local, professional theatre for a festival. Though I sent out a copy of my next play to much bigger theatres in London my next few commissions came through local, professional theatres and a real mixture of stuff, from twenty minute monologues to full length plays. In this time I was given a lot of time and support to develop work and improve and feel I jumped the gun in submitting to the big boys. I also joined writing groups, schemes and training events that the theatres were running which were valuable and led to other commissions and contacts.
After a break where I worked on other types of scripts my next play is being co-produced with a local outfit and a much bigger company, so for the first time my work will be toured by a big name out of the region - after that I am going to submit my next play to London, seven years after I first did! Hoping that the credits and recognition I have built up will help. So in my experience it worked out best to go small at first and build a name and credits up with companies who had a good record and name and who are open to supporting new writers. Professional theatre companies who specialise in new writing will always look first to their own region for writing talent and will be signed up to the Guild's theatre contract so you get the same pay and conditions as elsewhere. No harm in thinking super big at first but I don't know how realistic an option it is, though I got some good feedback and contacts, I think I would have been waiting a much longer time to see my work produced than I have.
As with local theatre keep an eye out for national theatres who run writing competitions and free script reading services as they are always worth a shot.
To add to Toothpaste's post I have sold ideas mainly based on a page outline/pitch, sometimes with an example scene/first act or to a lesser extent on an actual script but have never sold one by having to workshop/stage a reading first or considered it, but then my role is only as a writer I have no interest in producing or directing my shows and raising money for staging a show is different than paying a writer to develop a script. Most theatres want to develop the script with you and put their stamp on it, but whatever works for you is the way to go. Theatres like publishers have submission guidelines on their websites which they expect you to follow.
If you are sending 'blind' with no previous contact/discussion I think it is Ok to submit to more than one place at a time.
Good luck.