It's very important to get all your major suppliers under contract.
The contracts you write need to have all the detail in about everything you have verbally agreed with the supplier.
Things that should be in the contract
Are there constraints on when they can come on site? Do you want delivery by a specific date and time? Do they be off site by a certain time?
Does the contract contain a detailed list of everything they are supplying for you, right down to the battery fire exit signs on the tent? What are the power requirements of their equipment?
What if their equipment goes wrong? You may need them to supply an out-of-hours number with which to get them on site if there is a problem.
If this is your venue, have you nailed down exactly which areas you are using? If you are relying on their electricity to run your outside areas, this should also be in the contract (along with your power requirements). Do you have sufficient office space in the building? How many keys can you have to it? Will you be using their internet?
Things that should not be in the contract
You should not be paying more than 50% up front for anything. Otherwise you have no recourse whatsoever should it all go Pete Tong.
There should not be any clauses in the contract that you are not comfortable with. The supplier may assure you that they don't really want your first born child, no other customers have had their children taken away, etc etc. The correct response to this is "Great! Then you won't mind taking it out of the contract".
Negotiating the sticky points
If you're going into a meeting, make sure you know in advance exactly what you want. Know what price you'll accept, know exactly what you want from them, know what concessions you might make or accept.
The supplier may say "Oh, this is our standard contract, everyone has to sign this contract, we can't change it...". If you are not 100% happy with the contract, find another supplier. Make sure you are doing everything in plenty of time so that time pressure doesn't force you to go with someone you're not happy with.
If something you really need is a sticking point and you still want to go ahead, can you use it to negotiate a different concession? If you need a lower price and you aren't getting one, see if they will throw in something else that helps you out.
If you feel like you're being railroaded into agreeing to something you don't fully understand or you don't like, stop the discussion. Say "I'll have to discuss this with the team before I can go further". Now go and find someone else (previous organiser?) who can help you out and suggest a course of action, or even come with you to a meeting for moral support.
During the whole time, even though you may have disagreements, you need the atmosphere to be one of collaboration. They want your business; you want their services; if it doesn't feel like you're working together to achieve this in a way that works for both parties, then something's wrong. If the relationship feels hostile at the beginning, it's only going to get worse, and conflict with your suppliers is the last thing you need during the event.