With you being a student, I suggest looking for a club or taking a
class in theater costume if your school offers one. Free use of machines, and lots of people with experience right there in the room with you. My early experiences were with machines owned by family members and friends. You know the machines work, there's someone who uses them right there if you have problems, and you get to try out a couple different kinds and see what clicks with you.
With your two constraints (heavier fabrics and student budget) I'd go for a middle-aged or older used machine first. Do a little searching first, you will want a
local machine repair or sewing shop that can handle the brand/decade you end up with. My first was an 80s singer that liked to visit the repair guy every 3-4 years, but it did what I needed until I started getting interested in heavy denim, canvas, and leather.
The older metal body machines are usually great for heavy fabric. You'll want to learn how to repair and maintain them, they're more work than newer ones, but there's lots of
video and classes and online articles. They have fewer stitch options, and some of them only go forward. If they've got an electric motor, you'll want it checked (or learn to do yourself) before you use them much. Some of the old pot motor ones can have wire insulation issues. But nothing quite beats the feeling of opening up that wooden or leather case and pulling out an old metal workhorse :D
New inexpensive machines often have plastic internal parts and those just don't hold up with heavy materials. They typically have lots of built in stitches, and feet for all sorts of different tasks. Save your money, get a new machine with metal gears and all the bells and whistles when you've got experience and cash both.
And EDIT: Name them. Give each of your machines a name like you would a pet, it's a relationship.
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