Having built and rebuilt a few bikes not, I've gotta go with Pokey on the headset thing. Trying to install the headset may be the only thing that can actually damage the frame if one gets too hamfisted. I DID have a frame that required reaming the headtube. I actually tried installing the headset myself, even getting fairly vigorous with it. Pretty quickly I realized that something was not quite right. I paid a shop to install it and, sure enough, the headtube needed reaming. They also checked the bottom bracket shell and found it square and not needing thread chasing. After initial assembly and riding for a while to confirm frame fit, I disassembled the bike for painting. When I reassembled it, I decided to give the headset another go. It went in with appropriate snugness and gentle taps protected by a piece of wood. So I guess the moral is if it doesn't line up and go in fairly easily, STOP. I mean, it's got to fit snugly, but you shouldn't have to tap it very hard. Use a rubber mallet or place a board on it and tap it with a hammer.

DEFINITELY get a good book. I like Bicycling Magazine's Complete Guide to Bicycle Maintenance and Repair. Consider it a mandatory tool. Of the other things listed few are specialized tools and some you can buy less expensive brands that will work just fine. My suggestions

Pedal wrench - I don't have a pedal wrench. A 15mm cone wrench will do. For that matter any 15mm open end wrench will work on many pedals. However, on some the wrench flats may be too narrow for a regular open end so a thinner wrench is needed. AND, many pedals these days have a hex socket on the inside end of the spindle which allows the use of a 6mm or so allen key.

Bottom bracket tool - assuming you use a sealed bearing splined Shimano type, you can get an inexpensive Lifu for a few bucks from Nashbar.

Chainwhip - aka sprocket remover, a handle with a length of chain to grip a sprocket to hold the cassette still while you unscrew the lockring. A Nashbar brand works fine and is quite inexpensive.

Cassette lockring tool - Again, assuming you are going with Shimano hubs/cassettes you need a Park FR-5. This tool is only $5-7 anyway so get the Park.

Crank extractor - There are two types, one for traditional square taper bb spindles, a slightly different one for hollow splined Shimano spindle, you will need the appropriate one extractor. Some Shimano cranks come with self extracting crank bolts so you may not need an extractor, only an 8mm or so allen key.

Work stand - VERY, VERY nice to have.

These are about the only really special tools I can think of.

Here is what I suggest. Get a book, and work on the bike you have now. Take a few weeks to go over it from end to end. Pick an area, read up, get the specific tools, pull it apart, put it back. For instance, the rear wheel is a simple place to start. Get a lockring remover and chainwhip, less than 20 bucks total. Take the cassette off, clean it up real nice. Put it back on. Sounds simple and it is, but there is a technique to it to prevent damage to the cassette or lockring or your tools. I won't tell you. READ and learn. If your hubs have loose bearings you can clean and repack the hubs to learn about bearings.

Then try the headset, assuming it is traditional threaded. You don't need to remove the cups. Just read, take it apart, clean and repack the bearings, reassemble. If you don't have a pretty big adjustable wrench get one of the Park double ended headset wrenches with 30, 32, or 36 mm on one end and 15 mm on the other. Then you have your pedal wrench.

Last, do the bottom bracket.

If you are not willing to read, learn and try on your current bike I wouldn't try building your own. It will be a learning laboratory. Even if your current bike has all older traditional stuff and you plan to use all modern, actual installation mostly the same. You definitely need a book FIRST.
FWIW,
Raymond