It's important to remember that this budget is part of a proposal; it is inherently not set in stone, so it does not have to be perfect. You do not have to identify every expense that you will incur during the course of the project, but you need to show that you have considered, identified, and can estimate the major costs of the project.
If you don't have one already, I'd highly recommend creating a timeline (possibly in the form of a Gantt chart, for which you should be able to find multiple Excel templates or other programs to create one.) It sounds like you have a decently clear goal in mind (make sure you know what you mean by "improved," though that's mostly unrelated to this question.) But you also need to have a good idea of how you'll get to that end result.
Some questions I would consider asking yourself
- What stages will this project require? (Research, design, building, testing, etc.)
- How long will it take me to complete each stage? OR How long can I allocate to each stage? (The second may be more relevant if you have a strict deadline and certain things that you know will take X amount of time [shipping times, special orders for unique parts, etc.])
- What could prevent me from staying on schedule, and how likely are these events? (Out of stock parts, design challenges that may cause problems)
- What will I need for each stage, and will this incur any cost?
- Are any of these expenditures particularly risky, and how does this affect the budget? (Components that are liable to break during assembly or testing, travel costs that may be volatile)
You don't have to have the answers to all of these questions, but you should consider them. Some of them are inherently unanswerable; some you will only be able to answer after years of experience.
However, as you create this general outline for the project, you should start to see where the budget naturally comes into existence. Obviously you'll need to plan for building prototypes. But are these off the shelf parts, or are they things that will need to be made new, and if so, how do you plan on making them? Is the test you're going to run potentially destructive, necessitating multiple prototypes? These are fairly obvious questions, but consider some slightly less obvious ones, especially if you're focused solely on the new product. What kinds of things is this going to grab, and will you need samples for the testing process? This is an existing tool that you're improving, will acquiring a current iteration help you to understand it better, and will the company provide that or do you have to buy it? Are there similar products in existence from other manufacturers that could help you out?
Basically, you have to look at the project from as many angles as possible. And my first point is important enough to re-iterate. This is a proposal, you are absolutely allowed to change it halfway through the project, assuming you have a compelling reason.
Also, note that this is how I approach a budget, and how I've done it on projects I've managed or participated in in the past. But this may not be exactly what this company wants. Don't be afraid to ask your supervisor or whoever you're presenting the budget to what they're looking for. You're a student, they know that, they don't expect you to know how to do everything. You're there to learn, so take advantage of that.