I used Minwax colored stain - blue. It came out OK though not as uniform as I expected.
The tint in those things usually requires REALLY thorough mixing because those products tend to sit on the shelves longer than "regular" stains. I would bet money that your can says NOT to shake it up because it'll create air bubbles, but here's how you get around that. Shake the SNOT out of it (mebbe even throw in a big BB or something so it works like a spray paint can) to get that color off the bottom. Turn the can upside down (making sure NOT to have the cover loosely on....make CERTAIN it's on there good) so the stain works on the sludge color layer on the bottom. Do this a few hours before you're going to use it. This'll allow the air bubbles to come to the surface, and distribute the color throughout it. There will be NO way to even out the color otherwise. Then, when you're ready to use it, stir it up nice and good once again, only now you really DON'T want to shake it and create those air bubbles. When they refer to a "high quality" brush, they're talking about one of those higher dollar brushes (think $10-15+). The bristles are fastened WAY better and tend to not come off in your finish often, if at all. The reason they cost more is the materials, methods, and quality of putting the brush together. It's one of the few things where higher price almost always means higher quality, hence it's worth the few extra bucks (which also means you should take better care of it too, but that's another story

)
I didn't want a "wood-colored" stain because, I don't know, I wanted something a little unique. I applied 2 coats and it came out pretty good although some spots are lighter than others (this is what I meant by saying the wood was showing through). I'm using Minwax polycrylic as my sealant.
Absolutely nothing wrong with "a little unique"! I've used that stuff before, and it DOES turn out nice, but unless it's REALLY mixed well, you're almost better off going with an aniline dye...you can still work with that piece though. The "lighter in some areas than others" is from the pigment not being thoroughly mixed usually. The polycrylic is perfectly fine as a sealant as well.
If you're really not satisfied with the way it's turning out, I'd suggest sanding it back down (I know, it WILL be a lot of work

) and start semi fresh. I'd bet you're putting the polycrylic on there a bit thinner than you should, and something really important you mentioned is that you continued to brush it to smooth it out. Applying a bit more will give you more material (without excessive build-up) and once it's down, don't continue to brush it. It seems like it'll work, but in reality, you're working against the results you want. You're introducing more "lines" that need to be overcome, instead of applying it and letting it level itself.
To answer your specific questions:
- Stain: Minwax colored stain (blue)
- Poly: Minwax Polycrylic finish (blue can)
- Temps in your area while applying: It in my basement but it's hot as hell in NJ but my house has central air conditioning - it's comfortable. Probablt 72-75 degrees but I don't know for sure.
- Amount of time you waited AFTER application before sanding: Overnight for first coat; 3.5 hours for second
- I'm using a handblock with 220 grit (like th back of the can says) but I'm planning on switching to 1000 grit for the next 2 coats
- I think I'm applying about as thin a coat as possible with the foam brush. I go over it a bunch of times to smooth it out and I'd say it starts to get tacky after 10 minutes or so.
- I'm definitely not eating enough bacon because the last time I had it was wrapped around scallops when I was at a restaurant where my wife's parents and my parents were meeting for the first time. I got sick and spent the entire dinner on the tiolet in the men's room. This was about 6 years ago and I still can't eat bacon without feeling nauseous.

No problems truthfully on the stain and poly sealant, just need a bit of mixing and a touch more material. Try to imagine that you want to put on about
1/
16" of the liquid. Make sure you realize that in some areas you won't be putting nearly enough, so practice on a scrap to see what I mean. The small area will take less time for you to see the results, and less material. You'll see that you probably weren't putting enough poly on to level out. The stain doesn't need anything more than enough to do a color coat, and wipe off the excess after about 5-15 minutes or so, depending on how dark you want it.
Since you're working in your basement, I'd bet it IS about the same temp as the house, but WAY more humid. I'd prolly wait a bit longer before sanding - maybe a day for the first coat (or 2, it won't hurt, it's just hard to be patient

). For the second and following coats, I'd wait at LEAST as long as the first coat.
With the hand block, you flat out no ifs/ands/buts about it MUST be working in the direction of the grain (dunno if you are or not) otherwise get a random-orbit sander and use that to sand with.
Tacky after 10 minutes prolly means you're getting there with how much you want to put down, add a touch more, and ONLY brush it on (think "flowing" the liquid material onto your wood) once, and leave it. I PROMISE, it may not look like it, but it WILL level itself off better than the job you're trying to help it out with

Finishing requires planning, preparation, and patience. Skip any of them, and your finish MIGHT come out, and be good to you, but won't be the best it CAN be. It's one of the most annoying things for people like me with very little patience. My advice? Marry someone like my wife who likes to do your finish work

Hope all that helps and this ends up working out to your satisfaction. Let us know what you decide and how it turns out.