do i need a modem even after buying a router? Please clarify.
Also, what about TP-Link TL-WR720N?
There are two types of routers available, one is Broadband Router ( works with Any kind of external modem like cable, adsl, direct etc) and ADSL router( works only with ADSL phone lines BSNL, airtel etc).
low budget ADSL routers usually don't have WAN Port, so configuration it to work with cable modems is difficult or confusing if you cant get proper details from your ISP. where as broadband you can use any modem. cable modems will be given by the cable company only.
I feel that broadband router is suited for you.
720N has only two LAN ports and internal antenna. 740N has 4 LAN ports and External antenna. for about Rs. 200 difference, I think its better to go for 740.