When buying billiards tables, the first thing to consider is how much you want to spend. Pool tables are like cues, you can get fancy or keep it simple. Either way you go, the price goes up the more detail and customization are involved.
The main thing your looking for is a good playing surface,  quality rails and strong legs.

Billiard table sizes

For your home there are many options available. People usually either buy an 8 or 9 foot but the 8 is the most popular mainly because it fits the room better. A 9 foot table is considered regulation size and is the size you see on tv when you watch a professional tournament. Most 8 and 9 foot tables have drop pockets, meaning the ball goes in and stays in the pocket. Another option is to get a “ball return” table. When the balls go in the pockets they travel through the table and collect back at the foot of the table.
For homes, most people choose a drop pocket billiards tables. It just fits the decor of the room better and feels less commercial. But there are many fantastic tables in both styles.

Playing surface

Playing surface – the best playing surface is going to be on 1 inch slate with Simonis cloth. They do make thicker slate but one inch is the standard and most used in tournament play. Simonis cloth is considered the best felt for accurate play, takes english better and produces better speed.

Rails

Rails – Different companies have different names for their rails but the main thing is you want to get is solid wood (avoid particle board) with quality rubber for the best rebound. 
With these characteristics on a good solid frame you’ll have a nice playing table.
These factors will make the table heavier but heavy usually means a good playing table. 
I highly recommend the following brands: https://www.brunswickbilliards.com/, http://www.diamondbilliards.com/, https://www.olhausenbilliards.com/, https://aeschmidtbilliards.com/.

Pool cue info – https://billiardsguru.com/buying-a-pool-stick/

This is just some info to get you pointed in the right direction. Good Luck!