Soldering Station: Given you live in the US, you won't be able to do better on a $100 budget than a Hakko FX888D. If you'd prefer a knob to control it, there's the Weller WES51. Do note that both are entry level stations. Between the two, Hakko has the edge on tips; they have thicker plating (= longer lifespan), as well as more shapes than Weller's ET series tips for the WES51.
Now if you're willing to increase your budget, you can get improved performance. Next step would be a Hakko FX-951 for example ($267 in the US; uses cartridge tips that include the heating element and thermal sensor), so a fair jump in funding required; bit over 3x the cost actually based on street prices for the FX888D. And you can go quite a bit higher for a single iron configuration. Brands to look at besides Hakko and Weller would be JBC, Ersa, OKi/Metcal, Pace, and Thermaltronics.
DMM:LightAges offers some excellent advice IMHO.
Regarding the BM857, I actually own one. It's a fine meter, but do note it's an older model (value has diminished v. their newer offerings IMHO).
Pricing at the time of posting this (tme.eu):
As you can see, for $20 more, you can get a BM867 instead, which uses a dual display (very nice IMHO). The BM829 also offers dual display and similar features with fewer counts (6000 counts will do most anything you'll encounter). BM869 does as well of course, but the additional features pushes the price up. BTW, the BM86x series is the updated version of the BM85x series (single display swapped for a dual, which required a different case).
In any case, you get a lot for your money with Brymen.
For under $50, the Uni-T UT139C is a nice meter (has input protection suitable for mains), which is cheap enough you can get multiples (think simultaneous measurements), or allow for an LCR, such as the DER DE-5000 as previously mentioned. A fully kitted out DE-5000 + UT139C can be had for ~$200 shipped.
Oscilloscope:What's your budget, and what will you be doing?
I'm fond of CRO's, but a modern DSO is a lot more useful IMHO (screen captures for example). As per cost, you can get a DS1054Z in the US for $375 shipped (4 channels). Hack it, and you'll up it to 100MHz, double the memory, and enable all of the software features. Makes for one hell of a value.
PM sent.