Furniture, Wood and Cabinetry Finishing - Stain brands

So far I used two stain brands: General Finishes and Minwax.
Are there other brands?

Reason for asking. I'm trying to finish my oak cabinets in a espresso/wenge look. I found that the General Finishes water based Espresso stain is what I like. However it generates some grain lift. Since I have to do many doors and cabinets I'm trying to avoid sanding in between stain coats.
General Finishes has also a gel (oil) based Java stain. It goes on really well. No grain lift. The only problem: it is a little bit brownish.

Grain lift is normal when using a waterbased product.

For a listing of various brands available, I'd suggest a Google search on "wood stains"

I can understand your aversion to sanding - I try to avoid it whenever possible!!

Minwax is probably the most well known and is available most everywhere. There are probably as many brands as there are different paint companies.

Sanding is part of finishing!!!

Generally it is best to use only 1 coat of stain, it is hard to get wood to take multiple coats of stain. The correct procedure is to

#1- stain, wipe off excess, let dry

#2- apply sanding sealer or 1st coat of poly

#3- sand when dry, wipe off dust

#4- apply next coat of varnish/poly

#5- repeat #3 & 4

For vertical surfaces, how often should you brush back the stain, during the 1 coat, to ensure the top parts of the vertical surfaces keep stain in contact.

I usually brush the stain on the entire surface before wiping but for very large surfaces I'll brush with one hand wiping with the other as I go. The amount of time a stain sets on the wood has a direct effect on how dark/deep the color gets, so that also has to be kept in mind.