Just don't get a modern HP laptop, or any old ones for that matter. They're crap (personal experience). If you are not planning on playing modern AAA games then probably an older thinkpad would do. A friend of mine has an upgraded X1 Carbon gen 1, but i recommend something a little bit more modern for your usecases. I don't know about battery life tho.

refurbished thinkpad or dell xps. (buying something like a business model could save you money on the long run, because you'll be able to service the laptop later on. Instead of owning one of the new cheap consumer electronics that has everything soldered on and glued shut. And is generally made more cheaply.) Make sure to save enough money to afford a replaceḿent battery. The second hand one won't be at 100% capacity any more.)

My recommendation would be a Thinkpad

Preowned ThinkPad. You can get a 2018 or so X1 Carbon for $400 or less on eBay.

ThinkPads are generally pretty good. Got mine for ~£450 on eBay and it's got ridiculous specs for that price (4k display, discrete GPU, 2 nvme slots, 32gb of ram and an 8 core 3.6ghz i7)

I think it lasts about 5 hours of light use on Linux but like many ThinkPads you can swap out the battery so bringing a spare charged battery with you is an option if need be

i dont really know about laptops but maybe get a used or refurbished one?
at least two people around me buyed refurbished ones and had no problem

A used framework laptop

Or a used MacBook pro, don't spend more then $200.

Check out Swappa.com for a used laptop.... Got a very good deal on a thinkpad. Almost any laptop will work for what you do except for tinkering with almost everything which is kind of hard to define... Just avoid the Google Chromebooks

https://linuxpreloaded.com/ has a lot of linux compatible laptop-vendors.

Dunno where you are, so can't recommend a specific laptop. Guessing from your currency I'd guess NA and looking at linux-preloaded, boy are there few options from non-oligopoly vendors in NA :/ And what the fuck are those prices in NA? Laptops with 16GB for 3kCAD? Bruh.

You might have to shell out money to a corp that cares little for linux. Maybe these guys have a good list of affordable laptops https://laptopmountain.com/collections/linux

Ok probably your best option is a used Thinkpad, or maybe a Chromebook with the Chromebook distro, but if you want to do something crazy you could try the Pinebook Pro. It's a 14" arm laptop that comes with debian for $220. You might need some accessories, but it would still be <$400 for something new and interesting. However, it's a bit slow, and arm doesn't have as much software support. I think it could do everything a CS student needs, except browsing may be slow because web apps are so absurdly big and complicated now. Definitely would get more than 5 hours of battery.

https://www.pine64.org/pinebook-pro/

Maybe the new StarLabs StarLite. The CPU isn't the best but maybe it can do what you want.

Search on Flipkart, there's a few good laptops there. Don't know if they are full Linux compatible.

Take a look at this MSI Core i5 12th Gen - (16 GB/512 GB SSD/Windows 11 Home/4 GB Graphics/Arc A370M Intel ARC/144 Hz) Thin GF63 12HW-012IN Gaming Laptop on Flipkart

With points and a 1000 off coupon it comes in your budget.

I think you need to do something to make the GPU drivers work. See this reddit thread.

Try running Linux os live usb on it and see if everything works. If you use Linux Mint, i think you need to install kernel 6.2 since it's still on 5.xx kernel now.

Maybe buys something that you can expand in the future by adding extra RAM, replace the storage and exchange the battery. A lot of the modern laptops don't allow you to do any of those (planned obsolescence?). I know older ThinkPads are a good option but I think newer models are less serviceable. In Linux you can use tlp to tune up your battery usage and reduce the power consumption to the bare minimum. I would also recommend a second-hand ThinkPad, but just check if it is upgradeable.