Hi, I'm a beginner same of you, so I don't have experience to share with you. But I'm writing to share my approach to the same problem: the bootstrap.
And, as a side note, I tought that this thread could be the right one for my first message on this board, to introduce myself: I soldered my first radio when I was 8yo, but I just received my first (cheap charly) oscilloscope last week. In the while I became an IT guy with 50% e-engeeneering bachelor degree. About 5 years ago I went back studying (myself alone, no uni) where I left (flip-flops, digital networks) in order to fill a gap in the market... and I'm still working on my prototype. The time went so long because I can't spend money on this my little spare time passion.
I took the long way to bootstrap my lab: DIY. I've built my PSU, my oscilloscope, my 3D printer, my helping hands ... mostly using stuff I dig out from my scrapyard (20 years of IT rubbish), plus some jelly bean components, some arduinos, some buck-boost converters, some radios, some sensors; all stuff I bought 2 bucks at a time. And, of course, Dave, DaveCad, youtube, github, and all the good stuff you can find online thanks to the good people that share with us their passion.
I probably ended up spending more than your budget, and the things I've built are not much more than toys but ... they worked "until the next step". Last week I was building an SWR meter and ... I couldn't make it without an oscilloscope that is a bit more than the arduino-based ones; so I decided to jump my next 3 weeks worth of beers&porn, and I bought a 200 bucks hantek; and soon or later I'll have to drop it in favor of a 1000 one.
It's the classical hands-on approach that let you grow together with your stuff.
Just to make you an example: I've seen tons of opamp primers (note: I use Dave's docs as a reference, and then iterate around it using other good authors available online), downloaded a couple of opamps books, but I couldn't really grasp the opamps until I had to make my oscillotoy. And I didn't get them yet. But focusing the messy dry theory in my head, with a real project that I had the need of ... pushed me to get those tools, the opamps, in my hands and being able to use them. I guessed. Then I discovered the inamps... and the power opamps... and... I want to use them all! I'm hungry of something to make good use of that theory. I'm really looking forward to make the next step. Opamps are just an example. I got better understanding on how to buy the stuff I need, how to make PCBs: I just attached a purple laser on my 3D printer so that I can skip the idea to turn my old tabletop scanner into a UV lamp, or tweak a laminator, or stealing my wife's iron.
And I also learned to schedule the shopping so that I can buy in advance from China and the shipping delays don't interfere with my activities; because I manage multiple projects in parallel and pay attention on the parts I can buy with my little recurring budgets.
I'm still using my 15 bucks iron ... but I bought a tons of spare tips for it. Because it will take a will until I find all the parts needed to make a proper soldering station. At the moment I've found a 1000VA transformer, I've an old mini-itx case, a couple of arduino placed in the same 'soldering station box', and the 'soldering station' folder filling with projects I've found around. Once I decide which one to follow I'll put in the project box the proper power silicon, and buy the first JBL tip.
Again: you grow together with your stuff. If you don't have a timeline to follow, it is way better than allocate resources and procure all the stuff in advance. In some cases planning doesn't help much. Try, as an example, to make a list of opamps to have in the lab: you'll go crazy. The more kinds you buy, the less proper opamps you have in your lab and have to buy more.
cheers