I would add, Rode makes a mini(or micro?) boom pole for about 50 bucks. It's not internally wired, and it doesn't get super compact like more expensive ones, but it's pretty lightweight, extends pretty well, and has decent padding. And it doesn't look like a broom handle...

I think the 'ship' analogy comes from the fact that each brand has their own ecosystem. Once you've invested in native lenses, batteries/chargers, and cards, it can be expensive to just change brands when a new product comes along.

Yeah, that's a hard question to answer without any idea what you're trying to record.
I like my Rode VideoMicro for simple nat sound on-camera, and it's $50 or $60, and you don't have to feed it batteries (or remember to turn it off when you put it away).
If you need dialogue on-location, you'll want something much closer to the talent; I know some people pick up a Zoom H1/Tascam Dr-05 for about $100 which can work on a boom, or connect to a wired lav.

Anybody else cringe at 1:58 on the second video, where SD cards are just floating around with (relatively) heavy batteries? That looks like a recipe for something getting dropped/lost/broken.

I use the same (well, the ones with room for 12 cards), and mark one case with green gaffer's tape, and the other with red gaff tape. Cards in the green are formatted and ready to use, cards in the red case have footage, and the red case lives in the DP's pocket.
If, heaven forbid, a camera gets stolen, all the day's footage survives.

Not sure what your budget is (tiny, i know), but an ebay search for "15mm rod top handle" shows C shaped brackets that should connect to your rods and run up the side to a handle for about $65. not super cheap, but less expensive than a dropped rig