Since this is an open ended question I’ll just give you a basic rundown of how I would do it.
It seems that you would not need a cart plugin at all as you are not requiing a payment method. Therefore, I would use a simple contact form and have it send a copy to the guest and the admin. The would allow you to get the information you needed without worrying about payment.
There are a TON of Contact form plugins, If you are looking for free ones I recommend cforms II, contactform-7 and Dagon Design’s php Mailer. In that order. The hardest part with these forms will be getting your total to update with the amount of tickets. I think cforms II will have the most out of the box function to do this. You could also use a few lines of jQuery to do this such as:
$("#ticket_number").keyup(function () {
var value = $(this).val();
$("ticket_price").val(value*20); //assuming $20 is the price
}).keyup();
There are also commercial plugin solutions such as Gravity forms which will handle the pricing fields and JavaScript for you.
Hope that gets you on the right track.