You shouldn't sign any contract in the same meeting it is handed to you.
Never.
Ever.
Under no circumstances.
Even if they've got a wheelbarrow full of money sitting next to the table for you.
Contracts are hard devious pieces of work. It is vital you understand each clause and also the effect of clauses on other clauses. The clauses that modify other clauses are the most devious. That lovely clause on the first page that says the publisher will market the book to the best of their ability? It gets modified by the back page which says they'll put it up on a website.
Any agent, or anyone with a contract in their hand, should never be pressuring you to sign. They should be telling you to seek legal counsel, to research contract terms, to take it away and think about it for a while.
Getting a contract by email is great for you to read beforehand but you still shouldn't sign at the first meeting if you have questions.
If the agent says something and the contract says something else, the contract wins. If you hear the phrase "oh, don't worry, it's standard", then worry.
It can be hard to do but you need to look at contracts as though they already exist and you and the other party deeply hate each other. What can they do to you? What legal ramifications are there? If they have ripped you off, how much can you sue for or have they limited the liability?
Don't let the excitement of getting an agent overwhelm the rational you who needs to protect himself legally.