If you have the money (or want the debt), go to a "name" school for the highest degree you plan to pursue. If you set out to get a Masters degree, then you can get your Bachelors at a less recognized school (such as a decent quality state school). You just don't want to get the lower degree(s) from a low-quality school (e.g. no accreditation, bad reputation, degree mill, etc.), because that could impact your ability to get into the higher-level program. For the most part, once you have the higher-level degree, nobody cares where you started, so don't waste money and effort (e.g. busting your ass for good grades at a high-difficulty school, when an easier program somewhere else would get you to the next level) at the beginning.
If you aren't sure about the higher-level degree, or you don't always have good follow-through, go ahead and go to a bigger "name" school to start with.