Yeah, I think the numbers mentioned by the user above is right. Usually you will have to pay a deposit ten times the amount of the rent, but some builders may ask for Rs. 1,00,000 as deposit. Apart from deposit, some builders will also ask for maintenance fee which will be Rs. 1000 to Rs. 2000 monthly or lesser also. You can check out this link for more details about properties in Jayalakshmipuram - http://www.commonfloor.com/Properties-for-rent-in-mysore/cfct-mysore. There are many educational institutions in and around the area, and there also few hospitals in the area. The railway station is very close to the area, and because of the Hunsur Road which runs near the locality, the area has good connectivity to other parts of Mysore.
Oh, it's nice that you are moving to Jayalakshmipuram. I have lived in the area and I it is a very nice locality to live in. It is one of the prime areas of Mysore, and is next to VV Mohalla and Vontikoppal which are also posh areas in Mysore. If you are looking at renting a property in the Jayalakshmipuram area the rent can start at around Rs. 14000 and go up to Rs. 25000. You can rent a 3BHK apartment for around Rs. 14,000-18,000, while rent for a 4BHK will be between 18000 and 25000, and a 2BHK will be for around Rs. 10,000 to 14000.