Furniture, Wood and Cabinetry Finishing - Painting furniture

I have a bedroom set purchased in 1979 in cherry finish. I want to paint it white white. I took a drawer and sanded it but it had places where the sealer was still apparent. Then I used a stripper to remove the sealer. I used an oil based primer--Valspar One and Only Oil Bonding Primer. I probably put it on too thick because it is not even. I will sand it down and apply another coat. But, the real problems are:

1) Is there a better way to get a smooth, even finish on the furniture? I have 2 chests, a dresser and night tables...

2) What kind of brushes do I use to get the desired effect?

3)Is the primer enough or do I have to sand and strip also?

4)Can I use an exterior latex paint that will have better leveling properties?

Please note that I live in Florida. It hasn't been too humid yet, but it will be before I finish this project.

Ultimately, I want the finish to be smooth and white--no sanded edges, etc.

There must be some "tricks of the trade" that I don't know because every time I try painting furniture, I get frustrated because it is never smooth and sometimes the paint chips very easily. I want a durable finish.

First, unless there are lumps in the present ifnish you don't need to sand teh piece any more than necessary to dull the sheen of the current finish. You don't have to remove the finish - just rough it up.

Your choice of sealer/primer is a good one.

An exterior paint, either latex or oil is what I generally suggest because of it's better leveling qualities and greater durability.

Use a brush specifically designed for the paint you're using.

Overbrushing is the downfall of many painters. Lay it on, spread it out, 'tip' it off, leave it alone. "Tipping' is the stroke made with the brush nearly at right angles ot the painted surface, with just the tip of teh bristles touching. It knocks down the high spots without adding additional brush marks.