It sounds like you need a guided system as that is the easiest way to get hair-whittling sharpness (for me at least), and silicon carbide stones will handle all those steels. You'll also want something very fine, either a strop, lapping film, or ultrafine ceramic, since you're targeting "crazy sharp." Your budget is on the low end for this, so you may need to get creative.
I recommend you pick up a BORIDE Engineered Abrasives "kit" of CS-HD type stones as an affordable way into this, and find or even make a system to work with these. The "Fine" kit has stones in 320, 400, 600, 800, 1000, 1200 in the FEPA F scale, and the 1/8" x 1/2" x 6" size is about $19, more for larger sizes.
If you can stretch your budget for a
Hapstone M2 that appears to be a well made model, though I haven't used it. If not perhaps get the
Hapstone Universal Stone Holder for $33 and figure out how to build your own base for it. Or watch eBay for an Edge Pro Apex, but if you haven't used one it may be hard to recognize a (poorly made) counterfeit.
A strop can be as simple as a wooden paint stick, and if cut to 6" it can be mounted like a stone to a guided system. Many different compounds can work; my first was Mothers Mag & Aluminum Polish.