1) Anti-static mat and wristband.
2) De-soldering tools. (solder sucker and/or metal braid)
3) Positionable magnifying glass
4) Light and plenty of it.
5) Electrical tape
6) Wire (smaller gauges) and also jumper wires with alligator clips...useful
7) Resistor assortment (1/4 watt is sufficient)
8) Capacitor assortment (small ones...mostly decoupling caps)
9) Tie wraps
10) Soldering aids - stands with little alligator clips on 'em.
11) Power supply - could even be homemade (transformer, rectifiers, and capacitor) or a wall wart type.
12) Multimeter - even a cheap one is better than none.
13) Shrink tubing (and a really hot hair dryer....or just wave your soldering iron near it)
14) Decent soldering iron - it takes more skill to solder things with a low mass iron so heavy is good (heavy in the heat retetion parts such as the tip, that is...)
15) More stuff....like with cars or carpentry, it is always the little fiddly bits that grind your projects to a screeching halt and make you run to the store AGAIN.
You may say, "But some of those things are parts." Well, strictly speaking, yes, but I stock them anyway and treat them as consumables.