I love this question! Let me help you pick an oscilloscope.
If you're not designing a motherboard, but instead working on medium-speed (Agilent MSOX3054A. If $12k is too much, you can get the "lower" grade MSOX2014A, 100MHz, 8 digital inputs for an almost reasonable $3100. Agilent is the heir to the classic Hewlett Packard geeks all know and love, and the infiniivision x-series compares favorably to tektronix, dollar for dollar.
You need a multimeter. Just get the Fluke 87 and forget the rest. It is also useful to have a function generator and a frequency counter, even if you are doing low-speed digital/analog work. If you're doing RF work or designing analog amplifiers, you might also want a spectrum analyzer. These can get freakishly expensive depending on the type of work you want to do. If you didn't get a mixed-signal oscilloscope, look into getting a logic analyzer. For professional applications it's probably cheaper to just get the MSO.
Not as high tech, but equally important: a soldering station and a fume extractor. For working on mains-powered equipment, you are going to want an isolation transformer and potentially a variac. You will need some way to mitigate ESD in your lab, so look into grounded tables, heel/wrist straps, and ionized air blowers. Not the consumer grade stuff, you want something that senses static charge.
If you are the DIY type who doesn't mind getting your hands dirty, it is nice to be able to fabricate your own PCBs. You can get PCB mills but they are expensive and low-precision. Better to do it the old-fashioned way, in a printmaking studio. You need a UV exposure unit, a laser printer or inkjet that can lay down a high density of ink on a transparency (no recommendations, sorry, I'm still trying to find a good one myself), an etching tank with aquarium pump, and a sink. Just buy your PCBs pre-sensitized. For cutting and drilling you want a small bandsaw or shear and a drill press. You can Harbor Freight the bandsaw, but try to get a high-quality drill press with no spindle wobble or else you'll blow through drill bits like crazy. If you're OCD about this you might even consider getting a small mill, just make sure it has enough of a throat to handle the boards you want to work with.
If you want to do SMD in house you'll need a reflow oven, solder paste, some tiny tools, and possibly a low-power stereo microscope depending on your visual acuity.Throw in a hot-air reworking system too, they're essentially heat guns with chips that match common SMD packages.
You are going to be accumulating many, many tiny parts, so storage is essential. It will need to be versatile: bulk resistors are one thing, but over time you will accumulate reels of SMD parts, coils of wire, long plastic tubes full of DIP and other through-hole parts and all kinds of other junk. It has to go somewhere and stay organized. In my lab I use the tiny trays available at model shops for stuff that's not ESD-sensitive, but in pro labs I've seen large metal cabinets reminiscent of library card catalogs and flat files lined with anti static foam organized with mazes of dividers.
Finally you'll need good EDA tools, so be prepared to pay good money for professional grade software. Most of it runs on Windows so budget for a new PC as well. Cost is no object? Look into Altium Designer. It's the kind of software that doesn't have a listed price. Eagle is a realistic option although its user interface is like taking a time warp into the nineties. No free software I've tried can be cajoled into doing what I can routinely do with Eagle, so my advice is to accept that you'll be using a proprietary toolchain and budget accordingly. Good luck.