FlyinCat

First, don't feel obligated because of a discovery flight, but you may want to go with the independent instructor if they can fly with you a lot.

Second, package deals can be bad, in fact I'd be worried about handing over money in advance. Especially if you have no idea when you'll get an instructor assigned (some have waiting lists) or any guarantees on how often you'll fly, or whether the company will even stay in business. You might also get passed around from instructor to instructor as they get their hours and move on. That single instructor will probably be committed to completing your training. On the other hand, if you go with the independent instructor, you might not have options if you decide you get along (though you can probably switch to the big school if it isn't working out)

Either an independent instructor or a school can be a good option under the right conditions. You need to know:
-Is there a waiting list/when will I get an instructor?
-How many times a week am I guaranteed to fly? (The more the better, 3-5x week if you can)
-How many airplanes do you have/airplane availability? How much downtime do they normally have?
-How many students are assigned per instructor (if workload is too high, you may get substandard training)?
-What is your instructor turnover rate/How long will you be instructing before you leave for a better job?
-What times and days are you available to train me/does it line up with my schedule?

You may not be able to ask these questions directly (or they may not answer directly), but if you can talk to a current student or get a reference these questions are very important.