Most of the issues that music students face when applying to graduate school are the same ones that undergraduate students face - researching teachers, figuring out what you want from the programs, learning about ensembles at the various schools, etc. But there are some issues that are more unique to grad school applicants, and certainly some issues are far more important to grads than to undergrads. I'm going to create four "case study" grad music school applicants to look at the different issues that they bring up. All of these categories of grad applicants are based on the grad school applicants that we often see at Peabody, as well as on my own student experiences and the experiences of others I've met over the years.
#1: Plugging the Holes
This grad applicant has usually attended a solid undergraduate program and has a good grasp of most technical basics. He or she has also done a pretty good amount of playing over the years in his school ensembles, as well as probably participating in some summer music festivals. However, #1 may have a couple of technique issues holding them back from being ready for professional work. Perhaps they don't feel they've ever mastered their spiccato bowstrokes, or maybe they have difficulty controlling their vibrato. For this applicant, they need to focus first of all on finding the right teacher that can help them work through these issues, and then help them incorporate these changes into their solos and excerpts. It's probably not as important that they be at a school with a great orchestra program, or lots of fascinating music academics (see more on this below). Their two years at grad school will be very teacher-focused, so that should be their emphasis.
#2: Liberal Arts Convert
Applicant #2 went through a liberal arts program, planning to do their music on the side as a hobby, or perhaps as a minor. But at some point, they got bitten by the music bug and decided they wanted to switch to a music focus. Perhaps they did in fact switch majors, or perhaps they finished their original major choice while practicing more on the side. Their playing may be quite strong, and their commitment to music ensures that they will keep strengthening their technique. What they need more is the chance to work with a good ensemble and/or chamber music program, and also that they have opportunities to get some good music theory/history classes in. While they of course will seek a strong teacher, they should probably put extra emphasis on looking into the playing opportunities that they will have at various schools.
#3: On the Circuit
This applicant pretty much has it together professionally: good training, good ensemble experience, and good orchestral audition prep work. They are looking for an environment that will support them as they take orchestral auditions. They need a teacher who can be a great audition coach - a teaching skill that is very different from the skill set you need to work on more basic technique. Some teachers have both of these skills, while others are stronger in one or the other. They also need a school program that will not place a lot of demands on their time so that they will be able to practice, go to auditions, and hopefully seek professional freelance work to pay the bills. They should also consider school location carefully - flying to auditions in expensive and unpleasant, and choosing a school in the Midwest or on the East Coast will place them within driving distance of a lot more professional orchestras.
#4: Playing Catch-Up
Perhaps this applicant wasn't at a very strong undergrad music progam. Perhaps they just slacked off a lot in school. Perhaps their progress was hindered by illness, injury, or personal problems. For whatever reason, they may be arriving at their grad school application process lacking some core technical elements, or needing more ensemble experience. This person needs to first make sure that whatever issues were holding them back in undergrad are worked out before they go to grad school. They don't have the option of wasting time in grad school - they will need to hit the ground running and work hard to make it. They need to do what applicant #1 did, but on steroids - finding a teacher who can give their technique and musical knowledge a full-body workout, and making up for lost time in acquiring ensemble experience.
While of course no student will match any of these categories perfectly, many will find similarities with their experiences. Consider what you really need grad school for and make sure that you have as good a chance as possible to get what you need.
Now, for some general thoughts. Money is usually a stronger issue for grads than undergrads. Parents are often not able to help with graduate school tuition, and students already carrying loans from undergrad don't want to add on even more debt. Besides the standard strategies on getting financial aid, look for schools that are located in places with relatively low costs of living, and research what the gigging opportunities are for you, especially what sort of driving you might have to do to get to those gigs. Gigging can be relatively lucrative, but not if you're spending all your time (time that you should be practicing) driving to gigs in traffic!
Another way to reduce costs and increase your available work time is to look into programs with minimal academic requirements. Many schools - Peabody is one of them - offer some type of degree that offers all the performance requirements of a Masters' degree with few or no academics. This degree is usually cheaper and, for an applicant who doesn't have a strong need or desire for more academic work, can be a great way to get the teaching and ensemble work you need. Peabody's degree is called the Graduate Performance Diploma, but at other schools the name is different; be careful not to confuse this type of degree with an Artist Diploma, which is usually very competitive and oriented towards those contemplating solo careers.
Finally, consider whether grad school is really the right thing for you. If you can find a way to get high-quality teaching on a private basis, you might be better off freelancing - or even working at a non-music job - and practicing independently. This option certainly isn't for everyone, and you shouldn't undertake it if you're not extremely motivated and able to work independently.