Types of speakers to create nightclub style sound?

My thought would be that if you want to bathe the room in sound you need to understand the dispersion pattern of your speakers and then place the speakers strategically through out the room to achieve the amount of coverage that is desired. The advantage of pro audio speakers is that they are designed to cover large areas and not a single listening position so they should make the task easier to achieve, assuming that you are using the correct speaker for your application. Some are designed to work alone and others are designed to work configured in arrays. Another plus for the pro gear is that the cabinets are designed to be suspended and the electronics are fully balanced.

Without knowing anything about your space I would start with some type of 4 sub system on the floor such as an inline configuration that mijostyn uses or a DBA arrangement. You may need more depending on desired volume level and room size. I would then go with either a front fill type of cabinet (i.e. the small speakers that are placed on the front edge of a stage in large venues to cover the front rows) or an under balcony speaker suspended from the ceiling firing straight down. The quantity being determined by the area needing to be covered. You could use any sub that you like, I would not use anything smaller than a 12" and I would highly recommend balanced in's and out's and a sealed cabinet would be a must.

Integrating the system to your room will probably be your biggest challenge. You will need some type of speaker management tool like an XTA DP424 or maybe a dbx unit if they still make something, which is how you will connect your source to the speakers system, and some type of room correction either passive or electronic.

The best PA speakers generally have fairly wide high frequency dispersion these days, and if you're using something small-ish like little powered "phased array" type boxes (common in newer installations as the lower profile makes them easier to fly above the crowd, stacked or otherwise), and a couple of good powered subs on the floor someplace, you're in there...all controlled by an iPad from anywhere in the room...you're likely to be surprised at the overall sound quality of this stuff.

Maybe I missed it, but I didn't see any mention of room size as I scanned this thread.

I've seen some good suggestions:

Klipsch
Altec
Cerwin Vega
MTX
Ohm
... and a few others.

Pretty much any decent sized box speaker with a minimum 10" woofer works well.  Mount them in the corners horizontally at the ceiling to get bass gain.

I did this at my previous home.  Some neighbors loved me... and others hated me.

I also have this setup, (on a smaller scale), in the garage of my current home.  Great for informal "get togethers"... such as fish frys, hobo dinners, and yard parties.

Zu Omen Def. Done. 

This is not really in your budget range, but for the fun of describing what I have here, and it is in a 10,000 cu foot room with an 18 foot ceiling; it's probably better than any night club I have been too.  My brother, who is an audio/video engineer said that my system comes the closest to a live concert he has worked with the national bands.

Main speakers are Bryston Model T signature with PX1 external crossovers being driven with 2000 watts each from Anthem M1 mono blocks.  An Axiom Audio EP800V4 dual 12 driver sub with a linear power supply, no switchers here and to the left side.  An Axiom Audio EP500V4 to the rear, single 12 inch driver with linear power supply to the rear.  And A Bryston Model T subwoofer with triple 8 inch drivers and linear power supply to the right.  Total power in the system is around 7000 watts and trust me, you can not only hear very detailed music, you really feel it!

The largest improvement I made recently was the addition of a Whest PS.30 RDT SE 2019 phono stage... yikes!  the sound stage and imaging is simply incredible.  I have a huge collection of 1980's electronic club music and it just blows the windows out if needed.  The detail in the instruments is astounding. 

BTW, Axiom Audio builds all of Bryston's speakers, so the system is totally matched.  Again, this is not within your budget, but man is it fun to play this system with a party here.....