switch up input methods! if you're not at all a pen/ink/stationery nerd yet, I'd start cheap and gradually get fancier.
1) write more! no, more! more than that! keep writing! I have found that physically writing things down helps me remember them much better than typing or not recording them at all. I write in meetings, on phone calls, when I'm studying/learning something new, when I'm working, basically continuously. I think it's much better to have disorganized/messy notes than no notes at all - practicing creating not-so-good notes helps one record and organize information better. You'll figure out if underwriting / bullet journaling / other organizational schemes work for you as you try them.
2) you may have really different outcomes using different inexpensive pens. I used Papermate Profile ballpoints and Papermate Flair felt-tip pens exclusively for years before I got into fountain pens. I find needle-point pens inconveniently fragile and gel pens prone to smearing/smudging, but you might not.
3) How fast ink dries varies a lot depending on paper. Super cheap paper (e.g. generic store-brand notebooks) might absorb ink fast and "feather" (i.e. ink spreads around on the page) or "bleed" (i.e. go through the page to the next page). If you're using a ballpoint pen or a relatively dry ink, though, this might not matter. Physically smaller notebooks tend to be cheaper than larger ones - maybe grab the Goulet notebook sampler and a few different smallish ones from a local big box store to see what works for you. I really like Mnemosyne and Leuchtterm, but style and preference varies.
3) I have found that I notice the experience of writing more and write more carefully with fountain pens, also, the Platinum Preppy is amazing. If you want to get into fountain pens, getting a few Preppies, a converter, a syringe, and some ink samples is a great place to start. You can use the converter to clean out the Preppies when they empty, and the syringe to clean out the Preppy cartridges and refill the cartridges with ink.
I hope this helps!