I strongly recommend to buy as little equipment as you can because it's a misconception that you need to rush out and spend large, it won't help completing your projects and only take away funds that could be otherwise spent on assembly and parts.
Typically you would upgrade your bench as you see the need, but if you have a lot of money to throw at it then by all means say so and start spending up.
Do look for a couple of multimeters suitable for measuring AC/DC voltages rated for 1000V (avoid cheap Chinese when it comes to safety). You can find lots of information already here on the forums regarding brands, measuring voltage/current and biasing is easier with multiple meters. I'd budget at least $50 each for something secondhand. Your multimeter will be your most used piece of test equipment.
An audio signal generator can be had for free if you use a PC or cheaply using a home made circuit. On Ebay you can find cheap Chinese kits and generators starting at about $20.
Capacitance, ESR tester. Chinese on Ebay $20.
Oscilloscope, anything you can get your hands on, it needs to be two channel (which most are) to easily compare input to output.
Spectrum analyzer, a PC does a really good job, spectrum analyzers tend to be expensive so do not rush into this without doing proper homework on how spectrum analyzers work and importantly what you need to know when buying one.
Distortion analyzer, probably software again or later after you have made some progress you can consider upgrading.
Dummy loads can be expensive to make however a great "hack" is to use Utilitech 240V Universal (water heating) elements in different configurations to make 4/8/16 Ohm non reactive dummy loads. These were sold by lowes.com item #362342 for ~$9 each, see down below for a video explaining usage.
Google "Dim bulb tester" (aka the poor mans Variac), this is a reactive current limiting that allows you safely test your amp during it's maiden voyage.
Eventually you may want to invest in a Variac which allows you to slowly bring up amps to working voltages and also when used with transformers doubles as a handy way to get different AC voltages on the fly.
Read Chapter 3: Electrical Safety from this website until you fully understand every concept discussed.
http://www.allaboutcircuits.com/textbook/direct-current/Visit these 3 youtube channels and absorb some content.
https://www.youtube.com/channel/UCUEo3LPGD1gWfGJQoE0i1Gg/videoshttps://www.youtube.com/user/essoterric/videoshttps://www.youtube.com/user/Stratosaurus1/videos