What are the characteristics of the best indoor and outdoor soccer cleats?

What are the characteristics of the best soccer shoes?

Comfort, fit, sole material, breathability, and weight are the key aspects in choosing a suitable pair of shoes.
For indoor soccer shoes, the level of traction should be taken into consideration.
If you have a sensitive skin the hard material shoes will not be suitable for you as they will hurt your feet.
The Samba Millennium features a soft arena leather and a gum-rubber outsole for support and comfort.

Great stretchable kangaroo leather upper (Adidas Copa Mundial )
If you want something modern, you’ll fit into this one great (Nike Magista Obra/Opus)
If you have slight wide feet, you can get away with this pair, and you’ll be off done really well (Nike Hypervenom Phantom III and III DF)
The Nike Tiempo Legend VI shoe has a kangaroo leather upper which will stretch to your foot, and despite having a foam support cage, it will still stretch, because that foam structure does not reduce stretching abilities on the shoe. (Nike Tiempo Legend VI )

The blades or cones on the bottom of many soccer shoes to improve traction. The stud itself is often called a cleat and can be fixed/molded or detachable on the bottom of the shoe. Typically, there are three main types of studs: bladed, hard ground and round/conical.
The actual stud may be made of plastic, rubber or metal-tipped. However, check with your league before using metal-tipped as metal studs are banned from certain leagues.
Most firm ground cleats today have either bladed studs or a combination of bladed and conical studs. Bladed studs create less stud pressure over the course of a match. Bladed studs offer greater traction and speed, while conical studs offer a quicker release and greater stability. The conical studs offer more points of contact with the field, this stability means less risk of injury.
If you are playing on extremely hard, firm surfaces, hard ground studs are the way to go to ensure proper traction and a reduced risk of injury.
Source: Soccer Cleats on Quora

FG Means firm ground, correct. It is for real grass that isn’t too soft, but isn’t rock hard dry either. At the end of your playing session, it’s expected to have no mud, or a little amount of mud stuck to the bottom of your shoes. SG is soft ground, which is for soft, wet, muddy, real natural grass playing surfaces. Now, for your question. There are shoes for different surfaces, if you are playing on the turf that is like a rough carpet material, then you will want TF shoes, like this.
If you want a shoe to play on the type of turf that is usually a full sized field, with the little turf pellets that always end up in your shoes, you’re looking for AG-R or AG Pro or AG shoes. This is what the bottom looks like.
Reference: Quora