GA, but I don't think the teacher will approve .

Some UPS's don't use batteries. They use supercapacitors. The advantage is that they are not as sensitive to heat as batteries. Consequently, you will have more service life from supercapacitors. Many battery types have a limited number of charge/discharge cycles they can withstand over life after which their performance suffers. Capacitors do not have the same limitations.

You have to keep batteries charged up to keep them in good condition. Not so with the supercapacitors. Most systems are optimized around the available components. To do that, you need to know the characteristics of you components and the application or how they will be used. Since energy is generally not free, the amount of energy you need to maintain a state of readyness is also part of the design.

which is the best type of battery to use for UPS?

It depends on the application, but generally it is an AGM sealed lead acid battery of a size and voltage suitable for the UPS.

Why?

This is too broad a question to answer in a paragraph or two.

i mean lead acid or nikel cadmium or any other.

Speak to the manufacturer. <sigh>

Different types of batteries have different charging requirements for optimal performance. Lithium ion batteries have the highest energy density but that does not qualify that type for the best choice. Lead acid batteries have good performance at a lower cost.

Lithium ion batteries have to be charged properly or they may become a fire hazard. They have good charge storage characteristics where lead acid slowly deteriorates without a little bit of charging current to keep it ready.

The main point is that batteries are not interchangeable in a UPS because the charging circuit is designed for a specific battery type.