I think it's geometry?

[DebW]

Terms -- I think most of these I've heard/read, know what they mean, but "trail"???? What's that?

Handling -- cornering -- you mean I can take corners without slowing to a snail's pace and without using the entire road on some bikes? Flex? This would be how it takes bumps?

See http://www.phred.org/~josh/bike/trail.html for an explanation of trail. You will feel a difference in steering for bikes with different trail. The longer the trail, the more the bike likes to go straight all by itself. The shorter the more manueverable. Too short and most of us would have trouble handling the bike, find it "twitchy", or just have to concentrate too much while riding. The shorter trail bikes do let you take corners faster at higher speeds.

As far as flex, a longer wheelbase has more flex than a shorter wheelbase for the same frame material. More flex, less of a jarring ride on rough roads. But too much flex (especially in the chainstays) and some of your power goes into bending the frame instead of propellling the bike forward. But with new frame materials, builders are making bikes with a stiff drivetrain and a more comfortable ride. So frame geometry alone won't tell you much here without a test ride. You want to test ride by hammering up a hill in an almost-too-big gear to compare frame flex and power transfer.

So, am I understanding that perhaps a bike can be "amended" to make it work as I evolve as a rider, at least to a point? It sounds a bit like the things that would make a bike work for me as a beginner wanting a more relaxed position could be changed out so that I could have a more aggressive "stance" if I wanted it at some point? I can see where there would be limits to this, of course, but???

Exactly. You'll hear some riders here talk about "flipping the stem" to go from an upward slanting stem to a flat stem that positions the handlebars lower. Or you can replace the stem with one of a different angle and length. But if the bike is designed with a high head tube relative to the saddle position (which some bikes with slanted top tubes are) then you will be limited. Your handlebar position (at least when you start riding more aggressively) needs to allow for significant weight distribution to the front wheel when you are descending in the drops and climbing out of the saddle. And to give you more aerodynamics when you want it, like on a windy day.

DebW: "The slope of the top tube also doesn't matter, only the saddle position in relation to the bottom bracket." this relates to the knee over pedal spindle thing, yes? and how does it affect comfort? At times, I find myself scooching back a bit, and leaning a bit more forward, which seems to give me more pedaling power.

Yes, it's putting your body in balance over the pedals. As Lisa.S.H. recently observed when changing her stem length, which let her move the saddle to a better position and get weight off her arms. There doesn't seem to be any real science confirming "knee over pedal spindle" but it's a good starting place if there is saddle adjustability around that point. No one position is going to be perfect for every second of every ride, so you always need some "scooch room" anyway. Seat tube angle is more about proper body positioning over the pedals than about a particular geometry being better, though the type of riding could make steeper or shallower seat tube angles better (e.g. touring vs. time trialing).

DebW: "A sloped seat tube provides more stand-over clearances and supposedly produces a slightly stiffer frame." How can it make more stiffness? I understand the clearance issue -- oy do I understand clearance! (learned that young, and boy, you don't forget, do you?)

I'm not sure I believe the marketing hype for compact frames. The frame itself becomes stiffer if the seat tube is shorter, but then you sit on a longer seat post which has no cross-bracing. It should be stiffer for out-of-saddle sprints, I'm not convinced it's helpful for in-saddle riding. So I don't think you should go looking for a compact frame, but there's nothing wrong with one either unless that gives you a ridiculously long seat post. Just check the height difference between your saddle position and the top of the head tube so you don't limit your handlebar positions. You want a range of between level and at least 2 inches, maybe as much as 4 inches, handlebars below saddle.