All the advice is right on.
1. One wire at a time is preferred by some.
2. A harness kit is preferred by others.
3. Both end up being one wire at a time. One is actually installing one wire at a time, the other is hooking up one at a time. You do it in sections as spelled out by Otto and as you yourself said.
4. I prefer a harness kit. The universal prewired fuse box type. You don't want an "original" harness unless you are a purest.
5. You want everything to be fused.
6. Good time to convert to alternator if not already done. There are a few other "tidy-ups"/changes also.
I have done lots of wiring with a harness and one time without.
The prewired fuse box harness will not be more expensive than one wire at a time, Most likely you will spend more money buying pieces. You will have to buy EVERYTHING. No instructions, no connectors, no wire markings. You will have to buy terminals and contacts in bulk possibly. You won't be able to buy any of the "original" colors. The harnesses will have the more modern era Chevy colors.
The harness kits all have the same quality wire. You don't have many circuits/wires as said.
Post again if you need help in buying a harness. I have found that a harness is less work and a cleaner install. I will say that I have always removed the old wiring first. Keeping it in a sort of "harness" and putting it away for reference. Don't throw anything away. Take some pics before removal. As said, it is not a huge task and nothing to be worried about. We will help.
