Quantity   Component name
1 × a decent quality auto ranging digital multimeter I recommend either the ExTech EX330 $55 https://amzn.to/2EiNq70 or the Amprobe AM-510 $40 (residential) https://amzn.to/2EhPkF5
1 × a second auto ranging digital mutimeter so you can measure both voltage and current simultaneously; both of the above are good, or a cheapie is probably okay
1 × battery holders for 9v, 1.5v, etc eventually you'll need a variable power supply - but for now you just need some juice for your circuit
1 × A temperature controlled soldering station Hakko FX-888D, X-Tronic 3020, 862D+ (with safety mod http://bit.ly/2q5HhXT) - should run $50-100
1 × helping/third hands, hobby vise, breadboard holder, blue tack you need something to hold boards stable while soldering - if you get the old style alligator clip style, don't get the one with a magnifier and/or soldering iron holder. And in any case, you'll want to glue it to a wider base so it doesn't fall over
1 × flux paste, flux pens - to match your soldering iron tip type; some pens are refillable flux cleans oxidation and helps solder flow - if you choose to use something other than leaded solder, make sure your flux matches your solder - mismatching flux/solder/tips can cause tip corrosion and rapidly wear out your tip
1 × 63/37 rosin-core leaded solder - way easier to work and better results than lead-free It's mostly the rosin, not the lead, that is present in the fumes - avoid breathing it in
1 × fume extractor or a small fan/open window Move the air away from your face and avoid breathing in fumes
1 × Hakko 599B-02 Solder Tip Cleaning Wire and Holder Use this instead of a wet sponge to clean your tip - the wire is coated with flux and both removes solder and cleans your iron. Stop using sponges, do neither and cause thermal shock and accelerate tip replacement
1 × a flush cut soft-wire cutter This should only be used for copper wire - I recommend the Hakko CHP-170 $5 https://amzn.to/2EiAmyF
1 × replacement tips to match your soldering iron type if you choose to use something other than leaded solder, make sure your soldering tips match your solder and your flux
1 × a diagonal cutters for other wire any cheapie hardware store model will do, these should be a bit heavier duty than the soft-wire cutter
1 × hobby knife, #3 scalpel, etc. I stopped buying xacto blades in favor of #3 scalpels - much cheaper, sharper, they fit in more handles
1 × a small set of non-magnetic screwdrivers/bits
1 × a narrow smooth jawed needle nose pliers any cheapie hardware store model will do
1 × a slip-lock pliers any cheapie hardware store model will do
1 × 18awg-30awg stranded wire, 22-24awg is a good medium, sometimes referred to as "hookup" wire for wiring potentiometers and other hardware
1 × 22awg solid jumper wires you can find these with pins and without - either are fine, they should both fit in a breadboard
1 × a path to ground for discharging static as long as you and your components have a path to the same piece of metal, you should be good. You can discharge static charge by touching this piece of metal. Alternately, you can buy a two or three layer dissipative ESD mat, along with a grounding plate that can be connected to earth ground and a wrist strap/bracelet. Either your grounding plate or bracelet should have a built in 1MΩ resistor that spreads the electrical discharge over time so it's less likely to damage anything in its path.
1 × a small set of non-magnetic tweezers and DIP chip puller/extractor Optional for through-hole, but very helpful; mandatory for SMD
1 × self adjusting wire and cable stripper Optional, but very handy. I really like this model: $16.21 https://amzn.to/2q5a8LP Saves a lot of time, but it's also good to learn how to do this with your basic wire cutter.
1 × perfboard, prototype board after testing on a solderless board, you'll want to make commit your circuits to a stable board
1 × a solderless breadboard with at least 3 binding posts you can build this yourself or buy one like this https://amzn.to/2EiTSuO (includes jumper wires). Alternately you can just use a single breadboard and wire your power directly to the busses, or use a powersupply with pinouts designed for a breadboard, like this http://bit.ly/2q7yNiV