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A tribrach is convenient, but not really necessary if some other way to tilt the mirror is available.  A frame with three fine-pitch screws would work just fine (of course that's just what a tribrach is if you don't count the forced-centering clamp and optical plummet, which are not being used here).  An inexpensive one should be fine.

As for the tripods, again it was just convenience for me, since the surveyor type comes with a clamp in the head that's compatible with the tribrach.  The picnic table sounds okay as long as you don't sit on it, which might tilt it a little bit.  Photo tripods might be pushing it, though---probably too unstable unless you have a really massive one with metal feet.  Surveyor tripods do drift also---something on the order of 10 arcseconds over the course of an hour or two, more than good enough for AH use, provided the feet are on something solid such as concrete or stone.  A cheap and cheerful surveyor's tripod goes for about US$100.

I guess I'd still recommend a spirit level for general AH use with a reflective mirror, but that points out an annoying hole in the market for these things.  For some reason it's hard to get a spirit level of intermediate sensitivity (20 or 30 arcseconds per division) in a small high-quality metal package (3 or 4 inches) for a reasonable price.  A small machinist's level would be the right product category.

Cheers,

Peter