Who knows, can I use Cisco 1811 (or 18xx series) to establish PPP connection over Ethernet(PPPoE)?
If not, what model should I use to do it (Cheaper model is prefered).
Yes, you can absolutely use an 1811 to do PPPoE. You can also use a lower comparable line such as the 871. Both have dual-ethernet with managed switches. The 800 series has less capacity, and fewer features.