Help in buying a modem

I suspect you are confusing modem with router.

If you have internet, you already have a modem.

Most also act as routers -- but some are USB only or only have one connector for the computer. If yours is like the latter types you will need to replace it with a modem/router so you can distribute internet to other computers in the same hous (assuming your sister is in the same house).

A wireless router will enable her to connect using a wireless adapter. However, you need to consult your Internet Provider as setting up a modem/router requires particular knowledge. It may be best (if more expensive) to let them supply the hardware you need.