I've painted for over 40 years, mostly in oils but also took time to gain some mastery over the mediums of pastel and watercolor. I love your questions! They're the same ones we all have in the beginning.
My advice to you is to paint flat. You can always experiment after you "get good" with painting vertical, but there's good reason why a "watercolor easel" allows you to lay the paper surface flat. But in order to gain mastery of the medium, you really need to eliminate unnecessary challenges. Why make it harder? Painting flat gives you control; you can tip the board to direct where you want a wet application to dribble toward, or to avoid a dribble, etc. (typically you would be taping your wc paper to a board for this reason, and also to keep the paper from buckling).
And why, an inquiring mind would ask, would my paper be inclined to buckle? The answer is that the true magic of watercolor is the water! A ton of new painters apply the paint in a fairly dry manner, as if they were using tempera paint or oil paint, etc. That is not the idea with wc (although you can certainly utilize that technique, the result will look "dry" and sketchy, rather than wet and lush. The idea is to get the paper really wet, and then paint onto that wet surface, controlling what the paint does by how much you let that spot dry before painting onto it. Sometimes it is appropriate to really soak the entire sheet (you can dunk it in the bathtub or sink!), other times you can simply "paint on" a coat of clean water wherever you need a wet area to paint in.
I haven't read the entire thread, but from my teaching days I can guess some other questions that might arise.
Smooth paper (hot press) or textured (cold pressed)? I recommend cold-pressed (textured) paper. It is more forgiving in that the texture slows the flow a little, and mostly because it is more absorbent, so the paint and water-washes tend to stay where you want them better.
"Student-grade" (ie, cheap) or top-notch paint? This really depends on your budget. If you can realistically afford to buy good quality (not super expensive boutiquey brands where you pay mostly for the hype, but just good) paints, and your budget is such that you won't subconsciously skimp on paint because it seems so wasteful, then get a basic palette of good basic paints. Winsor Newton Professional WC is good, as is M. Graham, Daniel Smith, and actually Dick Blick makes a good line for a little less money. It's better, I feel, to get fewer colors of good quality. You don't need that many colors, really, because the number one skill to learn in any form of painting is accurate color mixing. If you buy a warm-leaning and a cool-leaning version of each of the primary colors (in light-fast pigments, preferably), plus black and a warm-leaning and cool-leaning brown for convenience, you will have all you need.
And speaking of lightfastness... I'm sure by now you have been caused to wonder about pigment toxicity. Yes, the very best warm-leaning reds (and therefore orange) and the best yellows (and therefore greens are the Cadmiums. And yes, Cadmium is toxic if you eat it, sand it down into dust after it's dry and breathe it, or put it into a cut on your skin. So don't do that. Same with Cobalt. Don't put your brush in your mouth. Just don't. And also, yes, true Alizarin Crimson is still the very best cool-leaning red you can get, and while not toxic, it's also known to change color in direct sunlight. Never hang an original watercolor in direct sunlight! The fake Alizarins don't make beautiful reds or violets. They are based on printer's inks, and they look it (IMHO). I have done testing for lightfastness putting Alizarin up against all the modern substitutes. They all change over a period of 2-3 years in direct sunlight (even sooner in Texas), so don't put the paintings there!
As for painting outside (we all have romantic ideas about how cool that is), again, I would urge you to work on your skills indoors in controlled conditions, and once you have amazing watercolor skills there, you can take your paints on location and watch your skills disappear. It's a whole other animal, painting en plein air. There are so many more variables, wind blows your stuff away, easels fall over, bugs and dirt end up where you wish they wouldn't, "well-meaning" people walk up and give you unsolicited (and unqualified) advice, the light on your subject matter changes so fast you can't keep up, or sometimes you just lose it entirely and it rains on you instead.
As for drying your palette, I recommend that you get one of the large plastic wc palettes, that have little "wells" around the edge to squirt your regular colors into, and a flat open mixing area in the middle, and a lid to keep them clean between uses. If you only paint occasionally and the paint puddles in the wells get dry, so what? You moisten them and they are good to go again. Dick Blick has these palettes, and for that matter so does (I assume; they used to) Hobby Lobby. Or you can use a sealable sheet cake pan, like Rubbermaid or something until you're ready to spend the $25 or so for a palette that will serve you as long as you are a painter!
Although a lot of folks start in WC because they think it is either simpler than oils or less expensive. Neither is true unless you plan to cut corners on quality or skip basic skill-building. WC is actually a more difficult medium to MASTER, it's just that a lot of people don't associate WC painting with mastery, but more with dabbling. You can dabble in any medium, but for mastery, WC has more variables to control, and allows fewer ways to cover or correct boo-boos.
This is getting to be a very long reply, so I'll spare you further musing from me, but hopefully this helps you get started. It's a rabbit hole. Have fun falling down it!
