Big fan of pencils for both office & study as well as sketching & artwork. Different erasers are designed to work with your particular pencil and paper selection, so there are a few issues to consider.
Graphite Hardness and Erasability
At the bottom of this post, I included a pencil grading test to show the effect of graphite hardness on how a pencil writes and erases. Generally speaking, softer leads are easier to erase, but they are also more prone to smudging (left-handed pencil users sometimes prefer harder leads for that reason). Harder H-grade leads are more smudge-resistant and give cleaner lines, but they tend to be more scratchy on the paper and are harder to remove once applied heavily enough to be easily legible.
The sweet spot between legibility and erasability is somewhere around the HB to 3H range (HB is your #2 pencil in the U.S. grading system — Graphite Grading Scales Explained). 2H is dark enough to be read clearly with minimal smudging while being easier to erase and correct mistakes.
Choosing a Pencil
The Dixon Ticonderoga yellow #2 pencil has been the standard pencil of choice since our school days. But with three lead grades (B, HB, H) available, you may want to try a few different hardnesses to find the level that works best for you.
But here is my top preference.
Many die-hard pencil fans swear by the Uni Mitsubishi 9850 for its smooth, dark lines and general utility for office and study needs. What caught my attention was the high-quality eraser that erases pencil marks easily and reportedly does not harden (a leading cause of erasers becoming ineffectual over time). I found the eraser on this pencil surprisingly good and erases easily without smudges.
Choosing an Eraser
There is a lot of variability in eraser materials and effectiveness and what they are designed to erase. The most common pink variety (made of rubber) tend to smear and leave a residue while the pumice can be punishing to the paper (think math homework filled with holes). But if you want to stick to what you're going to find in your local grocery store, the Papermate pink erasers have gotten notably better in recent years. Just make sure you keep swapping them out for newer erasers, as older ones tend to dry out and lose their effectiveness egregiously.
Erasers also come in soft vinyl (plastic), art gum, and kneaded erasers that absorb graphite rather than rubbing it away. I've been partial to gum erasers made for sketching and artwork, but I've been itching to try some of the newer plastics or even this battery-powered eraser that are reportedly extremely gentle on paper and meticulously exact. If you want to experiment with different materials, I would suggest the reviews at Guide to Choosing an Eraser… but if you want a one-stop solution, I would suggest the Uni Mitsubishi 9850 pencil I mentioned above. The pencil/eraser combination is surprisingly good.
Precision Erasing 2.0
You mentioned precision erasing to prevent you from losing entire lines when fixing up mistakes — from my aspiring graphic design and architecture days, I absolutely love these things:
Product Search: Erasing Shields
It may be overkill for some, but I find them indispensable.
Pencil Lead Hardness Test