Strong research departments like UMass look for three general things in a faculty candidate: Excellent recommendations from excellent people, evidence that you can do the job (e.g., publications, proposals, teaching experience), and a good fit in terms of research area and personality.
Good quality four-year institutions are looking for the same thing, but they weigh the evidence differently: Teaching experience, writing and speaking skills, and a general background are more important, but they still want research.
I'll describe specific qualifications in a minute, but let me start with what I hope will be good news. My impression is that the job market is not quite a buyer's market. I could be wrong, but I sense that there are many, many candidates, but not very many outstanding ones. UMass graduate students are better off than most when it comes to getting an academic job. This is because we are a well-regarded school with highly respected faculty, and I believe we have a reputation for producing good scientists with strong research and engineering skills who know how the academic game is played. Thus, search committees will look at you carefully and you will be competitive.
The ideal faculty candidate is a theoretical abstraction, but some people come close, and I'd like you to be one of them.
The ideal faculty candidate, let's call her Carole, has letters of recommendation from the best people in the field, and these letters are very strong. Carole has half a dozen letters, some from her committee, others from experts at other institutions. The letters say Carole has done creditable research on several topics and projects, all of it good. Her dissertation is important, timely, well-chosen, challenging, intrinsically interesting. Her treatment is scholarly, thorough, empirically-adept, well-engineered, insightful, produces good results. As a researcher, Carole is a self-starter, full of ideas, enthusiatic; she takes the initiative, has good judgment about research questions, works efficiently. These skills are complemented by a flair for writing and strong engineering abilities. Carole has worked cooperatively with faculty and other students in the lab on a variety of projects. She can be counted upon to give a good presentation to visitors with little or no notice. Carole has a huge capacity for work and the ability to keep several efforts going at once. Carole has a great personality and will fit happily into any well-adjusted faculty.