To try and answer your questions:
What is squonking and what are the pros and cons.
There are two basic types of atomiser used in vaping, RDAs (drippers) and tanks. The tank holds the liquid so it is simple to use. With an RDA the cotton inside the coil holds a small amount of liquid. This can he replenished by dripping e-liquid on top (dripping) or from a bottle contained in the mod which is squonking.
Who is squonking suited for.
Squonking is suited for all who want the advantages of dripping (flavour etc,) without the inconvenience of having to drip. you just squeeze a bottle.
What are the current best boxes in budget, mid and premium price range.
There are all in my opinion and are devices I have owned or do own.
Budget - Pico Squeeze
Mid - Runt
Premium - Armor mech or any of the Limelight freehands.
Availability of premium squonk equipment can be tricky, and you have to remember that it is the atomiser (RDA) which actually does all of the work. A poor mod with a good RDA will provide a better vape than a good mod with a poor RDA.
What do I need to know before getting into it.
You need to be happy with building your own coils. Need to be certain of what your vape style is such as MTL (mouth to lung, like smoking a cigarette), restricted lung (a draw straight to the lungs with some restriction) and DTL (direct lung inhalation with minimal restriction). The majority of squonking equipment is unregulated (in fact all of my favourites are), this means you need to be 100% sure you are happy with Ohms law and the implications of this with regards to battery safety.
As squonking is becoming more accepted by the mainstream we are seeing an influx of new equipment, especially from the Chinese manufacturers. Some of these are good, some not so good. If you are as I suspect are new to building coils and fancy giving it a go I would strongly advise a regulated device. I can't advise you which one unfortunately as I only have one regulated squonker, and I wouldn't recommend it as a starter device due to cost.