You should definitely look at the Jamjake K10 Active Stylus Pen. It is absolutely fantastic for the price! It has native palm rejection and connects instantly without Bluetooth, which is amazing for saving battery. You get about 10 hours of continuous active writing time and it charges via USB-C in just 90 minutes. Another superb option if you can stretch the budget slightly or find a refurbished deal is the Logitech Crayon Digital Pencil. It actually uses Apple Pencil technology, meaning it has zero perceptible lag and supports tilt sensitivity! The drop protection is also top tier, engineered to withstand up to 4 feet. The only downside is the shorter 7 hour battery life compared to the Jamjake, but the latency performance is just unmatched for budget note-taking.

Saw this thread earlier and wanted to chime in because I've gone through about five different budget pens over the years. People always forget to check compatibility first. Since you got an old iPad from your roommate, the very first thing you need to do is go into settings and find the model number. If it was made before 2018, most active styluses wont work at all. If your iPad is a 2018 model or newer, I highly recommend the Kingone Upgraded iPad Stylus Pen. In my experience testing these cheaper alternatives, it has the most consistent palm rejection and it magnetically attaches to the side of the iPad just like the expensive ones. It usually runs about twenty to twenty five dollars on Amazon. Just make sure to buy some extra tips because writing on glass wears them down faster than you think. Now, if it turns out you have a pre 2018 iPad, your options are limited because those screens dont support active palm rejection. Your best bet is the Meko Universal Disc Stylus 2 in 1. It is a passive stylus that costs around fifteen bucks. It has a clear disc on the tip so you can actually see where you are writing. It is not as fancy as an active pen, but it gets the job done for basic lecture notes without lag.

I went through this exact same search last year when I started my classes, and honestly, the budget market is a total minefield. You can get a decent one for under thirty bucks, but you have to be really careful because a lot of them are basically e-waste. Here are a few things I would suggest keeping in mind before you buy anything:

• Make sure to check the palm rejection feature. Some of the cheapest pens are just capacitive, meaning they mimic your finger. If it doesnt have active palm rejection, you wont be able to rest your hand on the screen while writing, which makes taking notes almost impossible.
• Be careful about the charging port. A lot of the older budget models still use micro-USB. I made the mistake of buying one and it was a massive pain to carry a separate cable just for the pen. Try to find one with USB-C.
• You might want to consider the tip type. Avoid the pens with those soft rubber or mesh tips. You want a hard plastic tip that feels like a real pen, otherwise your handwriting will look like a total mess.
• Double check the compatibility list in the product description. iPad compatibility is super specific, and if your roommate gave you a really old model, some of the newer budget pens might not sync up at all.