This should give you some ideas. Stocks tend to be different for skeet and trap. Scroll down for lower price items. https://www.gunsunlimitedomaha.com
I've shot skeet with both auto and pump, the pump ( Browning BPS 20) is much faster. Now I use a Citori 20 OU and a Browning BT-99. Neither requires me to pick up shells. Both at the time of purchase were under 2K.