OK, there are several options to choose from for class-E switching device in this frequency band.
1) Cheap, easy-to-drive, signal transistors: These transistors have a relatively high ON-resistance but very low gate and drain caps. So, they causes some loss but it's very simple to drive them even just by a microcontroller or any other digital signal generator. For example BS170 is an N-channel MOSFET costs around just 0.15$ (400 Toman)!
2) Power transistors: Their On-resistance is very-low but they need auxiliary drive circuits. Also, drain cap could cause trouble in class-E operation. They are more expensive than prior solution. Transistors like IRFML series or IRF540.
3) GaN FET: They are expensive but fast. Drain and gate caps are low enough to work well even at 13.56 MHz. Check http://epc-co.com/epc for more info.
4) RF transistors: They are not suitable for this band I think because of their high price.
Well, because you don't need much power, I think the first solution is the best and cheapest.