Although UMass has a reputation of being a party school, one can really succeed if he/she really puts in the effort. I just graduated this May and will be attending a top 10 graduate school in applied math this coming fall.
The stereotypes about the people living in the dorms as other people have mentioned are very very true. So think carefully about where you want to live.
In addition because UMass is a state school, many people already know each other from highschool. So it was difficult for me to meet new people in my dorm and classes at first. But that being said I've met some awesome people at UMass.
UMass is a very big place and no one is going to hold your hand. It is up to you to take advantage of the many opportunities the school offers. If you want to get involved in research or join a lab for the summer, try and email several different professors who you would be interested in working with. If you want to get an internship, ask upperclassmen and professors about where people from UMass have gone and see if they can hook you up. If you want to go to graduate school, go to office hours and ask for advice about what classes to take and what you should be doing in the summer.
Which brings me to my next point: get to know your professors well. Especially those you have for upper level classes. Don't be afraid to go to office hours. Although some professors may be really arrogant and unhelpful, many of the professors I've had were very helpful and patient.
One of the major downsides about UMass is the lack of resources. When I was thinking about applying to graduate school, there was virtually no information about the application process on the math department webpage. Also for internships/jobs, the career fair at UMass is terrible and career services is garbage. So the best thing to do is to ask professors in your department for advice and opportunities.
Advice about applying to graduate school: Ask more than one professor about which classes to take. Sometimes your advisor may not know which classes you should be taking. Also don't be afraid to take challenging upper level classes and even graduate level classes. When applying to graduate school, your grades in classes that are not in your major have very little weight.
Lastly, the most important piece of advice I could give is to start things early. Whether it be homework or projects, don't wait until the last minute to start something. The same goes for internships and graduate school. If you want an internship in the summer, don't wait until the spring to apply. Deadlines are usually in January, so apply well in advance and apply to many places. For graduate school, ask for recommendations well before the deadline to give your recommenders time to write their letters.I've enjoyed my time at UMass and despite the poor reputation the school has, it is possible to do well if one takes advantage of the numerous opportunities the school has to offer.