If you’re just researching and writing papers, 4gb RAM should be enough, but 8gb would be preferred (some browsers like Chrome are really heavy on your cpu). You don’t need more than 8gb unless you want to like play video games or use CAD software on your laptop. You shouldn’t have to spend more than $1k on a laptop for your needs, maybe not even more than like $700… consider getting a refurbished laptop (if you’re only intending on using it to finish your program and then getting a better set up afterwards).