My advice is, first and foremost, don't get too caught up on buzz. Almost all guitars with low action buzz to some degree. It's only ever an issue if it comes through the amp. That being said, I do all my guitar work myself and you do not need any specialized equipment or tools at all. You can get perfect results with stuff you buy from harbor freight.
Grab a set of small needle files, not diamond. Grab a straight edge. Get a 24" level, go for aluminum. Grab some 320-1000 grit sandpaper, rolls would be nice so you can cut to length, but whatever you have available works too. Get some double sided tape. You'll want to get some sharpies, some steel wool pads (not the ones with soap haha), and if you have a dremel maybe some brown polishing compound and polishing wheels in place of the steel wool. Also get masking tape.
Grab your straight edge and hold it along the neck. Mark off with sharpie where each fret is and use your file to make a notch for each fret. Now you have a notched straight edge. Adjust your truss so that it's flat flat flat (no strings of course). Stick 320 or 400 grit to the length of the aluminum level with double sided tape - no bumps or folds, make sure it's nice. Color frets with sharpie so that the tops are all black. Now place the level with sandpaper on the frets and begin sanding back and forth, trying hard to be hitting all the frets evenly. You don't need to press down at all, weight of the level is enough. Go slow and you'll start to notice that the sharpie is sanding off. Some frets (the lower ones) will still be black whole others will begin to flatten on top. You want to keep sanding ALL of the frets (even the ones now without sharpie) until ALL the frets are free of sharpie on top. You now have a leveled fretboard but you need to crown and polish.
Mask off your fretboard with masking tape, doing it one fret at a time is perfectly fine, crown the fret, pull the tape, next fret. Anyway, color your frets again with black sharpie. I highly suggest you take one of the 3 corner or flat files from your needle file set and use sandpaper or a belt sander to smooth one edge. This way you have a safe edge on your fret file. Purchasing a specialized crowning file will make this so much easier. With your 3 corner file begin to carefully file the black colored line on top of each fret to the straightest and thinnest line you can, while still keeping a line on top. What you're doing here is shaping the top of the fret to a nice thin point. After you've done all the frets you want to hit each fret with progressively finer grits of sandpaper from about 600 to 1000. Then finish off with steel wool or a dremel with polishing compound. You'll want the entire board taped off for this, with just frets exposed.
Buying the specialized equipment, even the cheap stuff from Amazon, can save a massive amount of time and trouble. Pick and choose what you're comfortable with. If you buy one specialized tool I would recommend a crowning file. I also highly recommend you practice at least once on a trash neck. And finally, I recommend you really study the process and understand what you're doing in each step. Understanding everything you're doing helps a lot. Trust me, I've ruined necks before because I didn't understand what I was doing.