Replacing your old light switch with a 20 amp switch isnt a bad idea. Connect a light and a fan to a new switch.

Leviton Decora Sureslide Fan Amp Incandescent Led Cfl Light
Light and fan on same switch. More energy and money. Using wire strippers peel an inch of insulation from the end of the black and white wires. Connect the black wire from the fan to the bottom terminal of the switch and the live circuit wire to the top terminal. Splice the white wires together and cap them. In both these cases youll have to run an additional wire. A 20 amp switch costs about 3.
Its best to make sure your light switch is up to carrying the load of both the fan and the light. Tie the equivalent wires together with wire nutswhile adding a new length of wire long enough to reach the switch you want active. Now when you turn on your light switch the fan will have power. Plus the existing switch will control both lights. If only the light or fan turns on when the switch is toggled then youre in luck. Some rooms remain dark and dreary with a single ceiling or wall light fixture.
Locate the switch cable which must be glued through the top or side of the box that serves the fan or the light. This new wire is called a pigtail. Not hard to do should take the sparky no time at all. Note that this is based on panelpower switch box fanlight. Twist the ground wires together and connect them to the green ground screw on the switch. Mount the fan and light and move to the switch box.
A standard 15 amp switch costs about 75 cents. In both switch box and fanlight box all grounds should be connected wire nut together. If you already have lights and a fan on two switches simply label the wires off each switch remove them from the switches and remove the light switches. And is it common to have the wires for both the fan and the light easily accessible behind the switch loop of twin and earth from fan to light and a new switch wire from the switch to the light so there is a switch wire for the fan and the light. To turn the fan and lights off separately use the pull chains on the fan. Stripping and twisting wires together and adding a wire nut takes only a minute or two.
If your configuration is panelpower fanlight switch box then the setup will be a little different. If both the light and fan come on when the switch is toggled the isolated wire is probably feeding through to another circuit. Get a new 20 amp switch. Adding a new light is easy because you can wire it to the existing light. Connect the black fan cable together with the black light wire and the black switch wire and cover them. Thats how you wire a ceiling fan with light to one switch.