You'll have to decide if you want an opaque finish, or something more transparent. The only staining I have done, I've gone opaque. It's not really all that much different than using a really thin, absorbing paint. Some of the grain comes through, but it's mostly about the color. You'll see the difference at the store, Depot has out samples that show the finish both ways. Pine isn't an especially fancy wood, so keep that in mind.
I've just used a paintbrush and been fine (but I use the conditioner). I know you can use an old t-shirt as well, I've just never done that. You can also buy bags of rags for next to nothing at Depot.
Avoid the all-in-one polystains. I've had good success using polycrylic finishes, IIRC polyurethane has a tendancy to yellow as it ages. You'll have to decide, too, what kind of finish you want for the poly. Gloss is a PITA to work with (the glossier the finish, the more any flaws will show). I'll usually use either semigloss or satin.
I've just used a paintbrush and been fine (but I use the conditioner). I know you can use an old t-shirt as well, I've just never done that. You can also buy bags of rags for next to nothing at Depot.
Avoid the all-in-one polystains. I've had good success using polycrylic finishes, IIRC polyurethane has a tendancy to yellow as it ages. You'll have to decide, too, what kind of finish you want for the poly. Gloss is a PITA to work with (the glossier the finish, the more any flaws will show). I'll usually use either semigloss or satin.