First, go into it with the idea that it's supposed to be fun, and don't worry about the little stuff. The instructor will get you back on the ground safely no matter what you do, so don't stress out about trying to do stuff correctly.
More important after the first few flights, I'd say you need to have reasonable expectations on what you're going to get out of it. A few "Free" flying lessons is going to be very very cool, no matter how you look at it or if it leads to an eventual pilots license. But after the excitement wears off a bit, you need to do the math to decide if you're going to follow through with getting your license. Not only is it pretty expensive to actually complete your license, there will be a temptation to buy a ton of fairly expensive equipment and books because although the gear is expensive, it's a fraction of the total cost of the license.
A common path to flying training disaster goes like this... You get your first few flights, and decide you're going to get your license. Great. You do the math and determine that it will cost, for example, $8000 to do everything including fly your checkride. Fine, that's within your budget for an investment that will last the rest of your life, so everything is cool. But then your instructor mentions that you will need to pick up some books and gear. You go to the FBO, and the books come to $200, but no biggie compared to $8000, so you get them. The next week you fly a different plane that has a very crappy speaker or you fly with a different instructor who doesn't have a spare headset, so you decide to buy a headset. After looking at the used and new ones, you compromise by buying the middle of the line david clark set for only $350. Pennies compared to the $8000 total, plus it's an investment, right?
But then disaster hits. Something comes up and you can't fly for a month so it takes a few extra flights to get your air sense back. One thing leads to another, and now you're approaching the $4000 expense point and you realize you're not halfway done. Oh crap. Re-do the math while trying to stretch the budget, and you spend another $1000 on lessons before giving up. And now you've spent almost $6000 and don't have anything but a used david clark headset worth about $80 and some books that are out of date because the new FAR/AIM came out and changed a few things so the study materials are obsolete.
How do you avoid this scenario? You must set reasonable expectations, first and foremost. And if one of those expectations is to accomplish your training on a budget, then you simply must keep price in mind for every single thing you do. Get a used headset. Try to find second-hand study materials that are still up to date. Rent the cheapest piece of crap airplane you can find for most of your training, because you just don't need to fly anything but a cheap piece of crap until you are very comfortable with the basics. Remember that every single minute on the hobbs meter is $$$ out of your pocket, so make every minute count (both on the ground and in the air) so you don't have to repeat anything.
Last, continuity is king when it comes to flying training. The more often you fly, the faster you'll pick it up and the better it will "stick" in your brain over time, which also means your training will cost less. Skipping flying is terrible for flying continuity - fly every week at the very least, 2-3 flights a week if possible, but if you really want to get it done on time and under budget, fly almost every day, 4-5 flights per week with time off to study and to let your brain match up the book learning with what you're doing in the air.
Reasonable expectations. Flying isn't for everyone and it isn't cheap. But if your expectations match the reality of your situation, then you are going to have a GREAT time flying no matter how much of it you end up doing.
