Public transportation in West Lafayette is quite convenient. GoCityBus is the service provider in public transport and is free for all Purdue students with an ID (which you will be able to obtain in your first few days here, as a visiting J1 student/scholar). You can check their schedules on their website or the app in which they provide real-time status of the buses.
Link to website: https://www.gocitybus.com/
Another way to navigate around campus is by bike or scooter—both are very common modes of transportation among students on campus. A bike would cost around $80-$100 for a new one and a used one starts at $30. Walmart is a great place to buy an inexpensive bike (and lock); also look out for special offers for college students. Please note that if you order a bike online, you need assemble it, whereas a store-bought bike is preassembled and ready for use. A good place to look for high quality bikes—both new and used—is Hodson’s Bay Company. Another option, with a larger selection of used bikes (check out the second floor) is Virtuous Cycles: http://virtuouscycles.us/.
Similarly, a scooter service is also available for students while on campus. Read more about BIRD on their website: https://www.bird.co/.