Should I go to a good graduate school (~#4-10) where I have a number of research options or to a well-known graduate school (~#1-2) where I have fewer research options but the prestige of the college name?

I'm approaching this from a social science background, where it is often possible to work on multiple projects at once. In that case, you need to think not only about how many options are available, but what the quality of those options are, and how many you can reasonably expect to take. If you can only take 1-2, having 3+ options doesn't make much of a difference. Sometimes what matters is how great the one project you can reasonably expect to spend time on is - especially if you'll be taking courses for a couple years. This can also be shaped by cohort sizes. If you'll be the only graduate your year, you can join a few projects and expect credit on all of them. If you'll be graduating with several peers who worked on the same projects, you might be fighting for credit and favoritism to get the letters you need. This could also change how many it makes sense to take. If there are 3 students your year, and 3 projects, it may make more sense for each student to work on 1 project for more credit than for all to work on all, and divide the work/attribution. Quality can fall into a couple of areas. A project can be great because it will make a huge impact, and answer interesting questions in one amazing paper, or it can be great because it enables a stream of research papers developing an important theoretical area (where one opportunity really represents 3-5 good papers). These streams can be important, because they can often be split, enabling you to start creating your own work, making clear your ability to do original research. These streams can also sometimes allow for a combination of theoretical and empirical papers, for even more bang for the buck. It is great to have your name on a huge and amazing paper, but if everybody associates that work with your adviser you might still be better off being lead/solo author on some smaller papers that can come out of a larger stream. You can also consider things like cost of living, quality of people you'll be working with (and I don't mean academic quality), and other things that will also have an impact on your life, and can make research much harder or much easier. Good luck - it sounds like you have some great choices available to you!

It depends on what you want to do. If you want to stay in academia, the only thing that matters is who your adviser is and how good of a job you do in your research.  If you want to go into industry, you'll make most of your connections through the people you meet at the conferences you attend, who will judge you on the quality of your presentations and publications. Having a good brand name behind you may get your foot in the door, but it won't guarantee any job offers. Now if you want to transition into another field, a good brand name is more useful. Big investment banks and consulting firms will love it. Software startups in Silicon Valley may be more likely to look at your resume. I have friends who've turned down big name programs like Stanford, MIT, and Caltech for programs that are perceived to be less prestigious by the general public, for very similar reasons as you. Their careers are all fine. In research, being around other people in your field is very important, especially when you get stuck and need someone to talk to. If there are only a couple people in your university who are working on similar topics it can be a frustrating experience.  But on the other hand, I certainly see the appeal of attending a highly-regarded school. So ultimately, I just recommend talking to as many different people about this and gather more data.

You don't need research options, you need just one right research path, and even that is too much.