Are you talking about the Boveda acrylic humidor? I'm not seeing a seal on that. But, I guess as long as they do a good job with the cuts it could probably hold humidity well.
20's the max, depending on the size of the sticks (in their pic it's 20x 5x50s). Looks like you can maybe go up from the 50 ring gauge in their picture, but you're pretty much stuck at a 5" length (internal depth dimension is 5 1/8") unless you put them in lengthwise, at which point you lose some of your capacity. But yes, in general, they're rated for more than you can typically cram in there.
I don't know that I would call this dirt cheap. If you want something small that you can have your stuff on display, I'd actually say to just go with a jar.
Personally, I keep the bulk of my stuff in tupperware. I stock my Xikar travel humidors out of them. I like the 10 ct size and can usually get a lighter and cutter in there as well.
Also, I just picked up a Xikar Cigar Locker + X0 cutter combo off cigarbid from their freefall auctions for pretty cheap. That just stays on the end table, but dedicated space for lighters and cutters, and the cigar compartment has a silicone seal. This would maybe be more ideal since it doesn't have as much foam that their travel humidors does, so it's not putting any sort of pressure on them, since it doesn't sound like you smoke often.
End of the day, as SimonPetrikov said, once you start shopping for sticks you'll probably move past the 10/20 ct mark. As you experiment, you'll find you have certain smokes depending on your mood so you'll end up wanting to keep a variety. And they work out to be cheaper when you buy them in quantity.